The CS55H will work with the cordless extension handset, and wouldn’t need a lifter since there isn’t a phone line coming in to the remote charger.
If a headset is needed for a cordless handset, any 2.5mm will work if there is a jack for it.
Technically the CS55H will work on the base phone using the included splitter. The handset must be lifted manually to dial out. After dialing, simply hang up the handset and walk freely with the headset.
CS55H is discontinued, recommend the AT&T Marathon