If I'm using an out of state address for mailing, will it affect moms benefits in California?

I live out of state. My mom in California in long term skilled nursing. Medicare is tied to social security meaning any address change you have to do it on soc sec site. If I change her social security mailing address to mine then Medicare uses this address. Will Medicare think she is not in California anymore? I don't want to mess up any benefits. I have electronic statements. But there has to be other people who take care of their parents stuff that don't live in same town/state. I really don't want that type of mail going to her like social security notices etc. Or someone think she is not in Calif. Currently I use a post office box but I want to close that in a few months as it's inconvenient to have someone pick up & mail to me.
Now she also has Medi-cal in California other states it's called Medicaid they already have me as her representative & use my address. I am just concerned about soc sec & Medi-care or am I worrying too much.