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

So my boyfriend has a son (they were never married and no court order is in place) his son is under the age of 2. The mother has been unsuccessful in her attempts to maintain consistent contact with my boyfriend. Her phone is always shut off for long periods of time due to non payment so he is unable to stay in contact with her and since has been utilizing facebook. In order for him to see his son in the past he has just had to show up at her parents and hope to catch her there. It has become apparent that she has moved and this became relevant after her not returning any messages for 2 months and also after speakin with her father who she lives half the week with other half with her mother. She never notified him of any sort of move not is she cooperating in letting him know where she has moved to. We did notify the police and they investigated and will be forwarding information over to the DA's office. Is this a case of parental abduction? She is also trying to claim child abadonement on his part but how is that when he tries to see his son an yet he can't because she never returns a message or phone call. She does not work, she does not drive and her only source of income is state/county assistance. What should he do? This situation is taking a mental toll on his life. Please help