Some say yes. I think it sounds wrong. The question of the possessive with the gerund is a point of dispute in English right now. I say use it when you can, but whichever way you do it, you will sound wrong to somebody.
So I can mean both things? "He reported to the police being mugged." In tis one it's clear that he's been mugged. There is no need to say "having been mugged"?