I am not sure of the answer to your question, though I can give you some pointers. I understand what you wrote to mean that an attorney in Virginia was
appointed as guardian/conservator of your girl friend. I believe that this guardianship/conservatorship is not transferrable to California. The guardian/conservator is a specific person, appointed in Virginia under Virginia law. Virginia law cannot determine who is a legally-appointed guardian/conservator under California law for a person living in California. Further, the Virginia guardian/conservator is not going to move to California, correct? So, as a practical matter, how could that Virginia guardian/conservator act in California? If your girl friend moves to California, I believe that a new conservator would have to be appointed in that state.
Is your problem that your need to get permission from the Virginia guardian/conservator to move your girl friend out of Virginia to California? Has the guardian/conservator refused to let her move? Have you, or others concerned with your-girl friend's well-being, demonstrated to the guardian/conservator why it would be in your girl friend's best interest to have her move to California? If you've done this and the guardian/conservator still refuses to authorize her to leave Virginia, your only remedy might be to file a court proceeding, challenging that decision.
Finally, the California law on qualifying for state Medicaid is out my area of expertise. I do not know if California would also require your girl friend to deplete her assets before she qualified for California Medicaid.