A transfer does not automatically carry your approved visitor status to the new facility. This is one of the more frustrating administrative realities families deal with and it can mean starting the approval process over from scratch.
In the federal system, visitor approvals are generally tied to the inmate's central file and can sometimes transfer with them, but you should always confirm with the new facility rather than assuming. In state systems the rules vary significantly. Some states have centralized visitor approval databases while others require a completely new application at each facility.
When your loved one is transferred, here is what to do. Contact the new facility as soon as possible to ask whether your visitor approval transferred or whether you need to reapply. If you need to reapply, ask the inmate to submit your name to their new case manager right away so the process can begin. Transfers can also come with a temporary visitation restriction during the initial classification period at the new facility, which can last anywhere from a few days to several weeks.