Another consideration to consider...
...is that sax players are notoriously "sloppy" when it comes to finger placement on a clarinet. They are so used to flopping a finger down anywhere on the touch pieces to make a key close that they have never developed the fine sense of finger placement that is drilled into clarinet players (soprano clarinet players, at least) from the get-go.
As a result, this is one of the few situations where I can in good conscience recommend a plateau clarinet. And that, in turn, restricts the recommendations to instruments produced by Leblanc.
Both the Leblanc and the Noblet lines had such horns in the past, although with the consolidation of the brands, that selection may have dropped off a bit. (They also cost quite a bit, no doubt due to other saxophonists discovering that you really do have to put those fingers in the right place.)
(Other than saxophonistus, the only other reason to consider a plateau horn is if you have some deformity or physical infirmity that would prevent you from using a standard Boehm horn. A guy who I used to compete with for baritone sax work had a badly broken and reset ring finger on his right hand, and he had no end of trouble playing the clarinet as a result. I suggested a plateau horn, and he immediately developed his skills enough to become a real competitor for work. Unfortunately (for him), he then died. His plateau clarinet was snapped up at once, while his YBS 52 remained unsold for several years.)
Although the player does not hear the horn in the same way as with a Brille horn, one with the open rings, the listener does not (in tests that we have conducted) notice any difference at all.
In the two 'clinical' cases that I've encountered, both players started on the plateau horn, and then later transitioned to the standard clarinet after they got the facility needed. A bit expensive perhaps, but a lot less frustrating.
If we are in a "single clarinet only" situation here (and the expense would tend to dictate that approach for most), then I would recommend that the putative clarinetist start out on a cheap and easy to find Vito instrument. The tone holes on a Vito horn are significantly smaller than on other instruments (to better suit them to slim young girl fingers, I suppose, especially for the third finger right hand - the designer was full of clever ideas like that), and will make starting up while covering tone holes for the first time a lot less frustrating.
Vitos can often be had for a C note or less - I've bought excellent examples for as little as $25.00 - and make for a good "clarinet with training wheels" for sax players. Once they've got the drill down tight, then they can dump the Vito and move on to something a bit more "professional".