Which is technically correct (even if not colloquial)? She is a friend of Jack's. OR She is a friend of Jack.
The second is correct and "preferable" by every "rule" of grammar.
So, as Svartnik points out, the second is the one you are looking for.
But really, the first is common enough that it should not be condemned.
She is a friend of mine -- she is a friend of Jack's. I'm not sure it's ridiculous.
It does work best for names (words) of one syllable, and the longer the noun phrase after the "of", the rarer the appended "s".
DOUBLE GENITIVE. The Columbia Guide to Standard American English. 1993
I steer clear of double genitives.
I think it's crucial to keep in mind always the intended formality level.
In writing, obviously, the apostrophe is poor unless in directly quoted speech.
I am sure the first version is correct (a friend of Jack`s).
The plain English is "she is Jack's friend". I think that's best form of all for a monosyllable.