Maybe you already know this but the fly is a very small piece that fits into the locks tumbler.
The fly can move back and forth and it is located so that if it is pushed forward, it blocks off the half cock notch so that the nose of the sear can't enter it.
If it is pushed rearward, it gets out of the way of the half cock notch so the nose of the sear can enter the notch.
When everything is working correctly, here's what happens when the set trigger is released.
1. The blade on the top of the rear trigger flies upwards and hits the arm on the locks sear.
2. That knocks the nose of the sear out of the full cock notch.
3. The mainspring begins to rotate the tumbler (and the hammer or cock) forward.
As this is happening, the sear spring pushes the nose of the sear back against the outside of the tumbler.
4. As the tumbler rotates and the hammer/cock continues to fall the half cock notch is rapidly approaching the nose of the sear.
5. When the nose of the sear is about to enter the half cock notch, it runs into the fly, pushing it forward so that it blocks off the half cock notch.
6. As the fly comes to the end of its movement, the nose of the sear rides up and over the fly (and the half cock notch).
Once this happens, the sear spring again pushes it against the outside of the tumbler as it rotates onward towards the 'fired' position.
When you move the hammer/cock to raise it from the fired position, the nose of the sear rides on the outside of the tumbler until it gets to the fly.
Further rotation of the hammer/cock causes the nose of the sear to push the fly rearward, exposing the half cock notch.
Once this happens, you will hear a "click" and slightly lowering the hammer/cock will allow the nose of the sear to enter the half cock notch.
If you try to raise the hammer/cock towards full cock, the nose of the sear will again, jump over the sear and continue to engage the full cock notch.
At this stage, firing the gun either with the unset trigger or with the rear trigger in the "set" condition gets us back to step # 1.
If the fly is missing or broken, it cannot block off the half cock notch so as the hammer/cock falls, the sear will enter it stopping all further downward movement.
You need to find out where the fly is and why it isn't blocking off the half cock notch like it should.
If it is missing or broken, get a replacement for it.
Until you do, you should NEVER use the set trigger to fire the gun.
Trying to fire the gun in it's present condition will break off the nose of the sear or it will break the half cock notch in the tumbler.
If either (or both) of these things happen the gun cannot be safely used.
A common question is, "Why can I fire the gun safely with the forward trigger even though my lock doesn't have a fly in it?
After all, military muskets and rifles that don't have set triggers don't have flys in their locks."
The reason goes back to step number 3 above.
Remember? As soon as the sear leaves the full cock notch, the sear spring pushes the nose of the sear back against the tumbler.
If a finger is pulling the unset front trigger it is pushing the sear nose away from the tumbler and compressing the sear spring.
Because the finger is compressing the sear spring, the sear can not move back against the outside of the tumbler while the hammer/cock is falling. The shooters finger keeps it away.
If held away from the outside of the tumbler, the sear cannot enter the half cock notch so the hammer/cock will just continue to fall to the fired position.