Laz will know the particulars for sure.. I read thru the synopsis, my take is you've got 180 days to sell them to a licensed gun broker, render them inoperable or register them in your own name.
DO NOT TAKE THAT AS GOSPEL.
There's been changes in the laws, some counties have additional restrictions, and/or the info above may not apply to your handguns.
IOW, wait for Laz to chime in here.
In your shoes I'd keep them and the original paperwork for them for my dad. If I was ever forced to use one in home defense, I'd explain the ownership trail to my lawyer and not answer ANY questions posed by the police. That means I would not even offer my NAME to the police if arrested for a firearms violation. Talk to a lawyer. Never the cops.
Good luck.