is it possible to convert generic animations to humanoid ones?

So basically, I have these animations I recorded in a mo-cap studio, and all though they were recorded on a model similar to the model I am using (a Fuse avatar), they are generic animations and work only on a generic rig (the customed generic rig that was made on my Fuse model in order to record in the studio). Is there a way to somehow convert these animations to work on a humanoid rig?

Yes - changing the rig is simple but getting the setup correct will take some troubleshooting using avatar masks and animation layers. Review both of these topics in documentation and learning material and you will grasp how to go about converting to humanoid while retaining the animations on all bones.