There probably is a link because trigger finger and mouse finger are usually the same and both actions run through the wrist tunnel (whatever that is properly called!). The name of the problem leads to thinking only of computer mice as the only cause, even though it's easy to address mouse-caused issues.

What has he done about it so far?

I have a worker that says he has it but he only does 4 hrs a day on a computer but his past time is shooting is there a link between the 2 — Don Ramsay

Do you know what sort of shooting he's into Don, and how frequently he participates in his past time of choice. Fired off a few rounds in my time (had a Firearms License before a Drivers one), didn't have any issues in that way until I had to slice start up rolls of plastic sheet into 50mm wide strips for reworking

What other work does he do, could that cause Carpal Tunnel and is the computer work aggravating it, rather than directly causing it?

he has gone to a physio for assessment, and working it from there

Then as per Steve H says, it would be a question of assessing all activities and how intensely those activities are carried out, that the computer work may aggravate rather than cause.

However, even 'only 4 hours a day' is quite a lot if there is a vast frenzy of mouse clicking-and-moving in that time.

As an employer doing the right thing, it may pay to carry out an ergonomic assessment of the work process, including anyone else if they carry out the same/similar role, and include any feedback from the physio if the employee is willing to share.

I don't have experience with mouse arm, but have dealt with carpal tunnel and shoulder strains which made driving a non-power steered car quite difficult.

I would recommend an ergonomics assessment to evaluate the impact of mousing on the problem. Yes outside of work factors might influence but have a look at how the individual is using the mouse. Are they resting their hand on the desk causing wrist extension while using the mouse - you should really be using your whole arm to move it. is the mouse as close as possible to the person? Number of clicks can also cause problems so does the software need reviewing.