I'm not 100% sure on this exact swap, but I am sure it has been covered before:
TA22 diff centre is the same as a T18 diff centre.
AE86 T-series LSDs will fit a T18 housing.
If the centre is small axle (can't remember if that's zenki or kouki) then the T18 axle splines will fit.
Only thing that spring to mind is that TA22 and T18 may have different track, but that is easily discovered with a ruler or some searching. Good luck
Hen
And dont worry about the whole S-series vs T-series. Yes, oz-spec sprinters had S-series diffs, but no LSD was ever made for S-series.