With a bit of reverse engineering, I think the 108215X will work. The 345 takes the 108308X spur sprocket and the 108215X rim system. The 445 shows the 108308X spur system. This is from the Oregon look up system. Since they take the same spur sprockets, maybe the oil drive gear is the same. I had the 353 and 345 apart recently and I can't remember if the pump drive was the same. There is a statement that other parts may be required, so perhaps you need a different oil pump gear.
I looked it up and the 445 takes the 503931801 oil pump gear. The same gear is used on many 340, 345, 350, 445, and 450 saws with the spur sprocket.
The 503892103 oil pump gear fits the 346xp and 353 using the rim system. I bet this gear will work on your saw but I'm not willing to tear my 346xp down to tell you for certain. Maybe someone will come along that has both systems apart.
Baileys summed it up:
Oregon Power Mate Rim & Drum for (.325" x 7) Husqvarna & Jonsered 345, 346, 350, 351, 353
This professional drive system includes a splined drum (clutch cup) with a replaceable rim. The rim floats freely on the spline, allowing the saw chain to align with the groove of the bar. Comes complete with .325" x 7 tooth spline. Drive sprocket bearing sold separately.
Note Requires a special clutch tool 31118 to replace. If you are converting a Husqvarna 346, 351 or 353 from a spur sprocket you need to purchase #503 89 21 02 oil pump drive gear as well. If you are converting a Husqvarna 357 or 359 from a spur system you need to purchase #503 91 27 03 oil pump drive gear. This rim & drum system has a small 7 spline and uses RSS rims. If you would like to run larger RSD rims, use part number ORF 108565.
Q. I have a 350 and am replacing the spur set up with a rim sprocket. Do I need a new oil pump drive pinion? I purchaced the 503892103 rim drive pinion but it is to large (15mm) to fit the crankshaft (13mm). The spur oil pump drive pinion is smaller (13mm) and rides nicely on the crankshaft. It seems that the rim clutch drum will drive the spur drive pinion but its a pretty loose interconnect.
A.
On the 350, no oil pump is needed. With this rim and drum system it should catch the oil pump as you don't need a different pump.