Just as an unusual suggestion: I have a pet attachment for my vacuum cleaner.
It's basically a soft rubber cylinder with a bunch of little rubber prongs
extending outward beyond the cylinder.

The problem, of course, is that most cats don't like the noise of a vacuum, or
even the airflow through the attachment.

But I had one cat who adored the attachment. Moe Lester really enjoyed being
vacuumed and it seemed to do a good job on any loose fur.

I use an ordinary wire brush on all the kitties. In fact, I use it on myself
as my fur is too raunchy for a normal people-style hairbrush to do anything
useful. I'm curious how the product recommended by several folks here differs
from that brush.

Art