I am keeping a LUMINOX series 3000/3900 for my son while he is in prison. Should the battery be removed for storage? If yes, can I remove it, & how do I go about doing it?

I am not absolutely sure about this specific model. But I do know there can be concerns with some due to the fact that the radioactive-gas filled glass vials are more susceptible to damage during the battery change. Also the O-rings should be replaced or at the very least lubricated if the watch needs to be stored for a long period of time.
A reputable jeweler should be able to take care of it for you for around $15 to $20.
Hope this helps.