Learn English – In a letter, what is the most polite way to ask for a quick reply

There are myriad ways to express a sentiment similar to the one you describe. Here are a few examples:

The above is purely for your information.

This is solely by way of information.

I write this simply to keep you informed of the situation.

. . . keep you apprised . . .

. . . keep you in the loop.

In my experience (mainly in the world of business), including this sort of phrase in a letter serves to clarify that the recipient is not expected to take specific action at this time. If you want a more general phrase to accompany an informative letter, you might also try:

I hope you find this useful.

By way of agreement with commenter jmoreno, I will add that the most similar practice I have observed in AmE (especially in the business world) is to introduce information that is included purely for information's sake. Often this will occur as early as the subject line of an email, which could begin with “FYI:” without appearing too informal.

The first is more polite while the second is more impersonal and better suited to a corporate or institutional setting where the recipient might not have a relationship with the writer.

Both are however too wordy; the recipient knows you're informing her by the fact that you're sending her a message. 'Asked for' is also too colloquial for a business or academic setting. I'd use 'requested'.

Also, the word 'completed' is ambiguous and not idiomatic (it could mean that it's been scanned but not made available for download, for instance). I would suggest instead:

"The document you requested is ready for pickup."

or if it is to be downloaded,

"The document you requested is available for download at [URL]."

or if you're sending this message with a PDF or other electronic copy of the document,

"Please find enclosed XXXXXX, per your request."