This problem has been bothering me for almost a week. I was hoping for that lightbulb moment but it's still dark in the attic, so here I am.

In the English coursebook, MyGrammarLab Advanced C1/C2, the passive form and its usage is handled in chapter 62, pages 270-273. Section 3 deals with the Passive infinitives and offers these examples.

1. 
   

   to be + past participle (to refer to the present or future)

   
   
   
   
   
   • (a) Children like to be praised when they do well at school.
   
   
   • (b) James was hoping to be accepted on the engineering course.
   
   
   
   


2. 
   

   to have been + past participle (to refer to the past)

   
   
   
   
   
   • (a) Stonehenge is the greatest monument to have been built by the ancient Britons
     
   
   
   • (b) This ascent is the first to have been achieved without the aid of oxygen
     
   
   
   
   

As a personal challenge to myself, and something which I normally do in my head, I wanted to convert the infinitive passive into the active voice without losing their original meaning but I've hit on some problems.

Are the following correct or have their meanings been changed?

1.(a)

    Children like to be praised when they do well at school. (Passive)

    Children like to hear praise when they do well at school. (Active)

I changed the original infinitive verb praise with hear, and I kept children as the subject of the clause. Is there another way?

If I add the agent, “adults”, I get the following: “Adults who praise children when they do well at school are liked.” which is wrong because it means children like adults who praise them. And “Adults need to praise children when they do well at school” but that omits the verb like from the original sentence and changes its entire meaning.

1.(b)

 James was hoping to be accepted on the engineering course. (Passive)

 James was hoping that they would accept him on the engineering course (Active)

I'm quite happy with this attempt, should I be?

2.(a)

  Stonehenge is the greatest monument to have been built by the ancient Britons (Passive)

  Ancient Britons built Stonehenge, the greatest monument in New Stone Age Britain. (Active)

I feel it is acceptable but the Present Perfect tense is missing – have built, and I can't figure out how else to do it

• 
  Ancient Britons have built Stonehenge which is the greatest monument in Neolithic Britain. (??)

This suggests that ancient Britons, the population that inhabited the British Isles circa 4,500 years ago, still exist today, which is not true.

However, I can make the Present Perfect fit for the following sentence.

2.(b)

  This ascent is the first to have been achieved without the aid of oxygen (Passive)

  This is the first time anyone has achieved this ascent without the aid of oxygen. (Active)

To sum up, I am having problems with converting 1(a) and 2(a) into the active voice. Can someone please explain where I am going wrong, if I am, it would be much appreciated. Especially seeing as I have to teach this stuff to a private Italian student.

There is another, simpler way -- at least for the first example or two. 

Converting a passive voice construction to the active voice always requires the inclusion of some agent.  Sometimes, it requires more. 

Children like to be praised when they do well at school. 

Children like someone to praise them when they do well at school. 

Here, the addition of an indefinite "someone" as the agent also requires the addition of an explicit patient.  Without "them" as the object of "to praise", the "someone" would seem to receive the praise rather than give it.  In this active voice example, "someone" is the direct object of the verb "like", and "to praise them" is the object complement. 

James was hoping to be accepted on the engineering course. 

Given "to be accepted" as a passive voice construction, "to accept" is the obvious active voice alternative.  However, the mechanical transformation used above doesn't work here:

*James was hoping someone to accept him on the engineering course. 

This shows one difference between the verbs to like and to hope.  Whatever hope does license, it does not license an object/complement pair.  One way to get past this problem is to use something that does license such a pairing. 

James was hoping for someone to accept him on the engineering course. 

In my dialect, "on" does not collocate easily with "accept".  I have no idea what it means to be accepted on a course, but I do know what it means to be accepted by a course.  If that's the intended meaning, then we can dispense with the indefinite "someone":

James was hoping for the engineering course to accept him. 

Alternately, we could simply assume a more likely agent:

James was hoping for the school to accept him in the engineering course. 

I suspect that the argument which to hope licenses isn't an object. 

It's a shame that such simplicity isn't universal. 

Stonehenge is the greatest monument to have been built by the ancient Britons. 

The passive voice construction "to have been built" has "to have built" as its obvious active form.  Again, the simple mechanical replacement fails, even though the agent is supplied in the original:

* Stonehenge is the greatest monument the ancient Britons to have built. 

The problem vanishes if we change not only the voice but also the finiteness:

Stonehenge is the greatest monument [that] the ancient Britons had built. 

Alternately, we could let the infinitive stand if we add some other finite verb:

Stonehenge is the greatest monument [that] the ancient Britons managed to have built. 

The original passive-voice infinitive phrase and the finite relative clauses have something in common.  They both work as direct, unlicensed modifiers of the noun phrase "the greatest monument".  This gives us a clue as to why the mechanical replacement fails. 

The active voice form "to have built" isn't available as an unlicensed modifier of "the greatest monument" when it's busy modifying its agent "the ancient Britons" (as a restrictive attribute, distinguishing this group of ancient Britons from others).  In turn, the full noun phrase "the ancient Britons to have built [it]" doesn't make a sensible unlicensed modifier for another noun phrase. 

? Stonehenge is the greatest monument of the ancient Britons to have built it. 

As a restrictive modifier of its agent, the active voice form of the infinitive phrase changes the sense of the sentence.  Perhaps other ancient Britons built a greater monument. 

By the way, "to have been built" is not a present perfect construction.  It's a non-finite construction, possessing no tense at all.  To make it finite, you must choose an appropriate tense, either "has been built" or "had been built".  In this context, "had" makes more sense. 

As long as you don't mind changing both voice and finiteness, converting the passive phrase to an active clause will work in most cases:

? Children like that someone praises them when they do well at school. 

  James was hoping that the school accepted him in the engineering course. 

  Stonehenge is the greatest monument that the ancient Britons had built. 

  This ascent is the first that anyone has achieved without the aid of oxygen. 

We've accidentally added an implication that someone does praise the children in the first sentence, which the infinitive versions happen to lack.  That may be reason enough to prefer the simpler mechanical substitution in those cases where it does work.