My question involves a child custody case from the State of: California

Is a custodial parent allowed to take their child out of the state or country without the other parent's knowledge/permission?

Supposedly, the father has sole custody.

He claims that the mother asked him to keep the child for a few days, and she never returned.

He claims that the court tried to serve her with papers but could not locate her.

(Trust me, the court knows her location.)

He claims that after two or three months of the court not being able to serve the papers, that he was awarded sole custody by default.

Is there any validity to his story?