You can switch the device that uses Personal Safety Button if you replace your phone, but it will require a few steps to set it up. Since the license is tied to the login and device, you'll need to update the details within the Settings, removing it from the old device.
Here's how:
When first logging in on a new device, you will be asked if you want to use this device within the Safety Button section.
Choosing to use this device will prompt you to transfer service to this new device and service will no longer be available on the old device.
You will be asked if you are using a new phone number.
If you select "No", service will now be active on this device.
If you select "Yes", you'll enter the new phone number you can be reached at in case of an emergency.
Once completing these steps, the In-App Personal Safety Button will work on your new device and be removed from the old.