When I pull the rear break lever, the cable contracts, but the lever doesn't return to its original position. How can I fix this?
If this is not enough information, please let me know. I will post a video or something.
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If it's just the wire that's not working, I'd replace the housing and cable for that wire to make sure there is no gunk or anything keeping it from moving freely.
If it's the brake, and it is a rim brake, the first thing to do is play with the screws that are on each arm of the brake. The farther in the screw is, the more tension is on the brakes spring which will help pull it back out. See if you can tighten that enough to get it moving enough.
If not check the mount points on the frame. A lot of the times there's a spring hidden inside the mount point which helps provide the return force for the brake. Generally it's three small holes in the frame which the spring will go through one, and then the spring is also pressing against some plastic housing, so if the plastic is damaged you'll need to get a new brake. If it doesn't looked damage, try changing it to a different hole to provide more return force and grease/clean the whole thing.
I'm speaking only generalities though, a picture or name of the brakes would be great.