At the outset, this is actually a Nevada jurisdictional question and not a California one. The general answer is that all 50 states do honor the judgments of sister states. However, the movement of the father to CA under CA law would be a significant change of circumstances that would allow either parent to move for a change of custody. Do be aware that at least for CA law, the issue of a move-away order may arise, but if his mother is the primary caretaker (regardless of time share), then a presumption would lean in her favor.
Simple answer: 1) yes, the judgment still holds up; and 2) the mother should move to change it as soon as possible.