That sounds good Rosie. It seems as though he has safety in mind as well. If bits of flue are falling, then, as someone has mentioned, there's always the risk of dangerous fumes escaping. A liner should take care of that. From the quote, I guess it's a flexible aluminium-based liner. (A solid liner would cast a fair bit more to install.)
I've fitted both types in the past. The flexible has a finite lifespan ................ maybe 10-15 years with coal or wood, but probably a lot longer with gas.
Sounds like a good move ............. sensible price too. They're quite expensive items.
Good luck :o)