coffeealex Rotation sense is the same - which was my doubt.
If the new motor fits inside the machine case with ‘its’ cap and bracket, I’d leave them as they are.
If re-using the old capacitor mount is needed to fit the motor inside the case, then by any means re-use it; it has no function beyond keeping the cap standing still! However, it seems to be secured by one of the studs that keep the motor casing closed, which means removing and replacing that too.