"Eu îi cunosc pe părinții ei."

Translation: I know her parents.

[zj456]

Which word specifically denotes "her" and not "his" or "theirs"?

[Caesar_Imperator]

„Ei”. That is the genitive-dative form of the pronoun „ea”.

Do not confuse it with the nominative-accusative form „ei” (meaning "they")

[KevinSmith777042]

If ei is genitive dative of ea then why is it introduced to us in this module on accusative pronouns? And what is ii (with a hat on the first i) which isn't in the table of accusative pronouns at all? I've just re-read the possessive pronouns section and now understand that ei is one of the female 3rd person singular possesive pronouns - that is its place here and why it indicates that it is her parents not his - is that the same as saying it is genitive-dative (we don't have the 5 cases in English as such hence je ne comprend pas!)...

[Scipio_V]

Îi is third person/accusative/masculine. Eu îi cunosc pe părinții ei. I know them, her parents.

[KevinSmith777042]

Why do i feel like ii with a hat on the first i didn't appear in the tips table?

[Thomas_Slo]

Because that table unfortunately isn't totally complete. I had to check it out on wikipedia for the sake of it.
The tips could/should have been done better.