In snooker the follow through is a very important part of the stroke and needs to be in a deliberate stroke not restricted by any movements.
The course of the follow through the cue must not move side to side and that is the reason the bridge length is important.
Keeping the cue as flat as possible at all times to create more power without having to hit the cue ball harder. A smooth deliberate delivery will have more cue power than a stabby quick action.
Your stance cue action and the dispatch of the cue ball all have to be connected and you need to work on each of these areas to have a consistent reliable action.
A good practice of the follow through is to line up the balls across the baulk line and play them into each pocket without the aid of a cue ball. You must line up each shot in your routine and make sure you follow though and remain down until the object ball reaches the pocket. Without the cue ball being in play it is much harder to pull back on your cue and this helps groove in a smooth consistent cue action.