Assuming they're using the world cup system (I have a feeling the PL system is slightly stripped back from that, but can't remember the details), the AVAR would be the one who's job it is to flag up the existence of a possible offside - but it would still be the primary VAR who communicates that to the onfield referee, and he would be communicating a decision that would be made by the two of them in tandem. If Jon Moss looks at a clip and doesn't think it's offside, then the goal wouldn't have been disallowed, regardless of what the AVAR did/didn't see.