Argthtjtr

Can we use borrow as I have in the above sentence in a sense like;

He borrowed (from someone for) me some money.

I wonder if there was a better way of expressing the idea that I am meant to.

Clarification: borrow there is not mistakenly used instead of lend.

Yes, in the proper context, that is grammatical. It would mean that he borrowed money on your behalf. It is colloquial, not formal. The use of such 'ethical dative' constructions with this verb is regional.

I have to thank John for helping me get this business started. He borrowed me a sizable chunk of change from his venture-capitalist buddies.

P.S. I think from some of the comments below that a few visitors to the site are concerned that I've given you a bum steer, some bad advice. You're not using the word borrow as some uneducated speakers do who use it in a non-standard manner, as if it meant "lend". An example from Nelson Algren's novel The Man with the Golden Arm:

Frankie dealt ... skipping Sparrow, who professed to be too broke to play...

"Borrow me a dirty sawbuck, I wanna play too," he asked the players on either side of him, twice each.

Each time each answered, looking straight ahead at the dealer's eyeshade, "Never play against my own money."

"Then borrow me a dirty deuce."

Sparrow was always careful to identify any money he was able to borrow as dirty, suspecting that he thus reduced the obligation slightly.

Don't use it that way, or people will think you flunked out of school.

Neither a borrower nor a borrower be.

--Polonius

You could, in theory, however it would only cause confusion in my opinion. For the sake of clarity, I would go with "he borrowed some money for me."

Wiktionary says:

7. (double transitive) To temporarily obtain (something) for (someone).

Quotations

1681 “Trial of Sir Miles Stapleton”, in State Trials, 33 Charles II, page 516:
Yes, my lord, he told me this in my own house; and I told him he might go to esquire Tindal, and I lent him eighteen pence, and borrowed him a horse in the town.

1866 April 20, Charles W. G. Howard, “Minutes of Evidence Taken Before the Select Committee”, in parliamentary debates, House of Commons, page 84, columns {{{columns}}}:
I went out and borrowed him a night cap; put him my night shirt on, and wrapped him in a blanket.

1999 August 1, “Ronnie Dawson, Singer, Comments on his Career and Music”, in NPR_Weekend:
My folks couldn't afford a guitar, so my dad borrowed me a mandolin one time, and I was just learning to play it pretty good and the guy that he borrowed it from wanted it back.

2006, Laurie Graham, Gone with the Windsors, page 116:
George Lightfoot seemed to have forgotten he was meant to be a Lost Sheep, and turned up as the Tin Man, but I forgave him, because he'd managed to borrow me a divine brass crazier from one of his bishop friends.

Still doesn't quite feel natural to me, but I'm not a native English speaker. Many people will probably have to think twice to understand who is borrowing what from whom for whom else. You're probably better off being more explicit:

He borrowed some money for me from ...

The shortest way (I can come up with) for saying someone who has borrowed money from another person or entity in order to lend it to a third party would be the following

1. He borrowed money to give me

The OP's sentence is, from a purely technical viewpoint, ungrammatical. Many native speakers would criticise (an English language teacher would mark it as being incorrect) and say that the past participle of the verb lend, i.e. lent should be used instead.

2. He lent me some money

The OP's suggestion, WITHOUT context, sounds ambiguous to me. Maybe nowadays it sounds perfectly acceptable in the US and in the UK, and speakers would not be confused, I simply don't know anymore. As I get older I see that life's little certainties diminish little by little.

3. He borrowed me some money

Did the subject, "he", borrow money from the speaker? OR Did "he" lend money to the speaker?

Adding the parenthesis (from someone for) is wordy, confusing and plain bad style, in my humble opinion.

P.S. if the parenthesis was added for the sake of clarity it should go after the sentence, not in the middle.

I think it's gramatically OK, but I'd avoid using it.

I've heard it used colloquially (Black Country, UK), but it had/has a slightly different meaning to the one I think you mean. In that "He borrowed me some money" would mean the same as "He lent me some money" or "I borrowed some money from him".
Likewise "borrow me some money?" can be used to mean "Can I borrow some money?".

That use isn't widespread [from my experience], and definitely informal. I'm not sure it's used outside that area ... but it does exist, so I'd avoid using it because it could be interpreted as that (not knowing the right word, so using a similar word in place ... or intentionally using the 'wrong' word)