As far as I am aware (never having been a customer of Beattie, for broadband), you should be able to perform a direct swap of the HH3 for the HH2.
I would advise that you perform a factory reset of the HH3 before you connect it to the line. Power it up, wait a minute for it to "settle down", then insert a straightened out paper-clip into the reset hole, press and hold until there is a change in status of the HH3's LEDs. Remove the paper-clip, wait a minute and then connect the device to the line.
If it fails to authenticate, you will need to copy across the credentials from the HH2 to the HH3.