Forward/Copy SMS to CiviCRM
I don't think that your standard SMS gateways are going to be able to cater to this. You could certainly set something up where CiviCRM forward SMS it receives from a gateway to specific people with contact details attached, i.e. someone texts central number. CiviCRM forwards that text to a specified mobile with the originating number prepended but that doesn't help for inbound SMS.

You might be able to acheive this with Telerivet, which allows you to 'turn any phone into an SMS provider'.

If the user was OK with downloading the telerivet app to their phone, it would allow them to forward any SMS sent and received to CiviCRM. I suspect that you can limit the numbers that have SMS forwarded to certain groups / contacts within the phone but you would want to do a bit of research on that.

Not 100% that this would work but might be worth exploring. It would certainly involve a bit of playing around and experimentation, but might deliver what they need.