I have read the post Enquire and inquire. It was illuminating, but I am unsure which version to use. I am an American, but am writing to a woman in England. It is a formal business letter, and the context is: "I am writing to enquire..." Is this appropriate, as I believe it fits the criteria mentioned in the other post, or should I use inquire?
Almost certainly OP should be writing to enquire, since he's presumably writing to ask about something, but not in the context of an official inquiry.
To the extent that there are two different words (and, frankly, many people don't distinguish), inquire conveys more a sense of formal, official investigation.
It's unlikely OP's correspondent would make that distinction and be alarmed if he wrote inquire (or indeed, be concerned about OP's vocabulary), but better safe than sorry – if in doubt, use enquire.