Can a Rogue use a heavy crossbow with sneak attack if the rogue player has the ability to use a heavy crossbow?
Sneak Attack requires conditions to be met in order to apply. They can be found in PHB page 96 or in the SRD.
There is no reason for Sneak Attack not to trigger with a ranged Heavy Crossbow attack, if all requirements are met.
Sneak attack (PHB p.96):
The attack must use a finesse or a ranged weapon.
A heavy crossbow is a ranged weapon and so may be used to sneak attack when used as such (rather than an improvised weapon for instance).