Is it appropriate to use acronyms in business-related e-mails?

No. That’s my immediate response, seeing that a colleague recently complained that she read several in an e-mail and didn’t know what most of them meant.
An e-mail is a business communication tool that should be treated with the same respect as any other business document you
write. It’s inconsiderate to run the risk of confusing and frustrating an e-mail recipient just to save a few keystrokes.
Subject lines are the only place you should put abbreviations, because it might help tell your story and entice people to read your e- mail among all the clutter. Even then make sure it’s something you know the reader will recognize, like “FYI.”
With that said, business etiquette is not about a set of iron-clad rules. It’s about being considerate. So if you know the recipient well, and you’re sure they know that “FWIW” means: For what it’’s worth; or “TTYL” means: Talk to you later – go for it.
Younger generations have grown up with instant messaging and texting on phones. It’s common in texting to use abbreviations like, “BRB” for “Be Right Back” or “ROTFL” for “Rolling on the Floor Laughing.” But business communication should be totally different.
In personal e-mails to friends, write how you want. But in business, I high recommend not using abbreviations.
FWIW – For what it’s worth -Why risk annoying the reader, by forcing them to take time to look up an abbreviation or ask someone. If you insist, make sure it’s common, like RE: short for “concerning.”