Here is a step by step guide should your buckle fall off of it’s vintage belt.
Take a look at the back of your buckle, there is most likely a side that is less open as seen in the far left image above. This is the side you will permanently attach the belt to. Then take a look at your belt to identify the front side and back side of the belt. The back side will be flat and will most likely have a seam on the back of the hook as seen in the far right image above.
Slip the belt onto the buckle side we chose in the first step (less open side) with the back side of the belt facing up as seen in the far left image above. Now press down the back side of buckle to keep the belt hooked permanently.
If you are unable to do it with your fingers, grab a pair of pliers and a cloth. Place a cloth between the pliers and the front side of the buckle as to not scratch the buckle as seen in the far left image above. Now pinch shut. I hope this has helped you repair your vintage belt. Feel free to contact me with any questions.