Force emoji to display as it was sent I understand that apps exist to change one's global emoji font,
and therefore send and display emojis universally in a specified emoji font.

Does any software exist
which checks the font in which an emoji was sent in an SMS and
which then displays the emoji in that specific font,
without changing the set of emojis the user uses by default?

(I use the standard Android set of emojis,
and I am all for varying sets of emojis;  however,
I suffer from constant miscommunications when receiving IMs
from someone with, say, an iPhone.)

I'm preferably seeking a solution which does not require that 
I know the sender's model of phone,
I use a specific messaging app,
the sender also install the solution on the sender's phone.

(Even so, I'd like to hear all options, if any exist.)
Emoji's are special "character" codes. Really, just numbers that all* software agrees that a particular number means a particular emoji.

Custom "fonts" change how those are finally displayed to the user—how exactly each emoji looks. But under the hood, it is just sending/receiving a number.

So when another user gets a message including an emoji number, it loads up the fonts that user's device thinks that emoji number matches.

No other data is transmitted besides that number.

Therefore no, there is no way (through standard SMS/MMS/IM protocols) to supply which custom "font" you used.

The only way for this to be possible if both sender and receiver agree to use a special communication tool that adds the extra "font" information to the message. 

I'm not aware of any specifically do this. Others may correct me on this. But either way, there isn't a standard communication protocol to share an "emoji" font choice.

** Well, most software, agrees on emoji codes. There are some companies that disagree in some cases. This is a known issue with emojis. There is a standardization committee, but again, not everyone agrees with them. Keep hope though; emojis are more standard these days then they were in the past. And maybe the standard will extend to allow for communicating custom emojis (or whole custom emoji fonts) over the protocols? Hopefully, one day in the future, we will have a utopia of emoji agreement from all!