How to move a shelveset from one branch to another in TFS

You're going to have to start by installing the TFS PowerTools for TFS 2013 (or whatever version is appropriate for you). Once you have the powertools installed and the tools added to your PATH (if they're not already added by the installer), run a command similar to the following in the command line:

tfpt unshelve /migrate /source:"$/ProjectName/Branch" /target:"$/ProjectName/Targetbranch" "My Shelveset Name"

This will unshelve your shelveset into your new branch for you.

WARNING: Before you do this, make sure you're unshelving into a clean branch with no Pending Changes, otherwise you could inadvertently overwrite or otherwise lose important changes.