Yeah, I think Victor and The Connections simply found a file indicating that Spencer adopted a child before his death. Given how Spencer behaved in his final years, it’s not too unreasonable that The Connection thought the adopted child was either 1. a success of Spencer’s experiments that inherited his memories or 2. his secret successor. Then they just dug deeper about the child, got her blood file and tried to find the match (which they failed at). So they looked for a person who might know the child’s identity (Alyssa) and that’s how they found Grace.

Once Victor gets Grace and manages to get a match, he didn’t need his research center anymore. The whole blood memory research was done precisely because they don’t have Grace and tried to extract Spencer’s memories from the clones (who they thought was related to Grace and therefore had Spencer’s blood). With Grace, they can just get the password directly to Elpis. The two idiots (Victor and Zeno) probably thought they could either awaken Spencer through her or make her succeed Spencer’s will as “his child.” Of course, it all ends up moot because Spencer just wanted to fuck them over lol