I am not sure EXACTLY what you want to do, but I'm "hearing" that you would like son to live with your mom (his grandparent), and she and he would like that as well.
You can execute a valid "Authorization Agreement". You can authorize grandparent relative to performing certain acts (for example, consent to medical treatment, obtaining insurance for child, enrolling in school, authorizing other activities, employment etc.)
There are requirements for the agreement (in writing, must be sworn before notary, possibly court approval, etc.) SO, consult a local family law attorney regarding executing an Authorization Agreement.
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This is something you need to discuss with a family lawyer. Your conservatorship may limit your right to turn your child over to your mother. You will also need to make sure you follow the right steps to make the transition smooth for your child.