There aren't two separate permits, i.e he won't have two separate ones. What I think it's saying is that the employer has had the work side approved so it's now a question of the authorities being satisfied that your cousin isn't a master criminal or some such. I don't think it will take too long, but he needs to organise his Type D visa for entry into Switzerland asap. Here's the procedure for the whole process:

https://www.bfm.admin.ch/content/bfm...ensablauf.html

I think he's passed the cantonal stage and it's now moved on to the FOM end of things.

Whether he'll make Christmas may depend on which country he's having to apply from for his visa.