I know at least some MGB used a LH-type OD, which was never fitted to Triumphs. Since that OD does not appear to be an A-type or J-type, which were the only ones fitted to 'big' Triumphs, most likely it is an LH.
So I believe, at the very least, you would have to fabricate a mainshaft and adapter housing to fit it to a TR gearbox. Within the realm of possibility, certainly, but not easy. Whether an LH would stand up to the torque of a 2.5L is a different question.
If you're interested in such a challenging project; it might be more interesting to adapt an auto box from a 82 Supra. Only 4 speeds, but the lockup torque converter and .688 overdrive should produce excellent performance. Even more interesting would be the later Supra box with electronic controls (making it much easier to reprogram on the fly).