I use an XLINK BT to do what I believe your customer wants -
(no affiliation, just a satisfied customer).
The XLINK is wired to a CO port on the Norstar ("line 3" for me, which is Ring Only on most sets, and Ring & Appear on a couple). There's a version that can connect "in series" with an existing CO line, such as for residential or single-line systems.
The box is linked Bluetooth to up to three cellphones and connects automatically when they are in range, usually on the shelf above where our chargers live. Incoming cell calls can be answered from any of the Norstar sets. Works well, even including Caller ID. Outgoing access to cellphone is also possible, including selecting which cellphone to use.
Which reminds me - apparently the XLINK can also bridge Skype calls from a connected computer to the phone system, which I intend to test. Not that I have any need for this, but it "sounds neat". Yes I am a phone geek, and proud of it.