Is there a single word for a "friend of a friend"?

I am looking for a word that I could use instead of "friend of a friend". On certain occasions, it happens that you may want to talk about a friend of a friend with someone else.

In such cases how would you refer to this friend?

If you have met the friend of a friend in person before, you might call them a "mutual acquaintance".

A mutual acquaintance is a friend or acquaintance whom you both have in common — i.e. the friend of your friend.

Acquaintance is the word you're looking for (as Andy already noted.) By definition, "acquaintance" refers to a person you know of but are not close to. If you wanted to be more specific you could add an adjective like mutual or casual.

If you feel "acquaintance" is too formal for your needs, then restructure your sentence to use a possessive phrase (i.e. "friend's friend" or "Joe's friend") to avoid the prepositional phrase but keep it casual.