The 'wir erlauben uns' bit is just too grovelling for any UK invoice text, so I'd leave it out completely and write something like: 'Re. your quotation no. 123 we are invoicing for the following services:'

Is 'to invoice' also used in AE for sending a bill?
I was asked to correct a form letter for a friend and her company had wanted to write 'I permit myself to invoice...' Sounds way too strange to me, or?
The solution from earlier won't work here as far as I can tell.

yes, invoice also works for AE. Maybe: Enclosed please find an invoice...

That sounds good, but I'm not sure it would work here, since company A is sending expert B a form letter for B to fill out and sign and send back asking for the money.
What do you think dude, would that still work?

You might want to put some of the wording in here; I'm not sure what exactly it is you're looking for

That's my problem: Their sentence is "I permit to invoice an expense allowance of..." which doens't work at all.

Hey Werner! Does that mean I can and should get rid of the 'erlaube ich mir' part in my German bills? What do you write instead then?
And the text for my friend then is probably 'just':
I am billing/invoicing (you) for ... Or?

Hi there, I have stopped using that "ich erlaube mir" part. In most cases I just send an Invoice with no real text line in a letter at all.

Some times I send a cover letter with some information to the client which then ends:

Eine Rechnung für meine bisherige Tätigkeit füge ich bei.

end of story

I guess I've been totally wrong in my usage of the phrase - I use it to tell the author the amount of the bill in the actual bill, not the cover letter.
Such is life, at any rate, the bills are still paid, thank goodness.

No examples. But it's the sort of form letter I send regularly. Business correspondence is cool (in the old sense of the word), crisp, to the point, polite, brief and factual.

Exactly 'erlauben us' is far too grovelling. This is business not begging or cap-in-hand!

Dieser Faden ist zwar schon uralt, aber ich habe gerade folgende Rechnung auf dem Tisch:

Wir beziehen uns auf die oben genannte Angelegenheit und erlauben uns, Ihnen mit beigefügter Kostennote unsere weiteren erbrachten Leistungen zu berechnen.

Das "erlauben uns" ist noch lange nicht ausgestorben! Aber für mich klingt es auch immer, als würde man sich entschuldigen, weil man sein Geld haben will.