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As they are both the same phone model, you should be able to register the additional handset to your new base unit.
just bought a BT4600 and wondered if my old BT4600 additional handset would work with it.
Yes, if they're the same model, it'll work. You need to set the base station to pairing mode (usually long press on Page button; but check user guide). And on your additional handset, go to the menu to find the Register settings.
If you're asked for a PIN, it's usually 0000 (unless you've changed it previously).
For any additional handsets including the BT4600 contact the BT Spares helpline on 0800 980 8999.
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