When is it approriate to use actonyms and emoticons in business communication?
Emoticons, never.
The only time you may use acronyms in business communication is
when they are business related. For example, "POS" is an acronym
that means "point of sale" and refers to the cash register--retail
management may use that acronym in business communication. Each
type of business has its own jargon.
Acronyms like LOL and BTW are never to be used.
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The above answer suggests that an actonym is the same as an
acronym, which is not always so.