This video show steps to move a shelveset which is created in one branch to other branch in Team Foundation Server. So using these steps you can move your code from one branch to other without manually copy pasting the code. Use this command to migrate shelveset:
tfpt unshelve /migrate /source:"$/ProjectName/Branch" /target:"$/ProjectName/Targetbranch" "Shelveset Name"
Make sure that you have installed TFS power tools before using above command.