Unfortunately, it is not possible to move the charging station from your spot to another car park on request ☹️
However, you can check out the available spots equipped with Recharge charging stations. There's sure to be one near your new home!
If you live in a property managed by a landlord and requested the installation of a charging station through your landlord, you can ask to have the charging station uninstalled so you can take it to your next home. You will have to pay an uninstallation fee.