Questions & Answers about Hún tilkynnir vinnufélaganum sínum um nýja frestinn.
Because tilkynna commonly takes a recipient in the dative: tilkynna einhverjum = inform someone / notify someone.
So vinnufélaganum is dative singular definite of vinnufélagi (coworker), meaning to the coworker.
It’s the combination of:
- the definite article suffix (the -inn/-inn/-ið system, which changes by case), and
- the dative singular ending.
In other words, vinnufélaganum = to the coworker (not just to a coworker).
sínum is the reflexive possessive (from sinn) and it refers back to the subject (Hún).
So vinnufélaganum sínum means to her (own) coworker.
If you used hennar, it would typically suggest the coworker belongs to some other female person already being talked about (i.e., not reflexive to the subject), depending on context.