Using the guide from larsks, I was able to do this using SourceTree.
Created a branch in the destination repository
Added the source repository as a remote, by hitting the Settings button and adding the source repository.
Branches from both repository now show in the branch list. I used the merge tool to merge a branch from the source repository to my new destination repository's branch.
Resolved any conflicts using either SourceTree or my IDE
Commit the changes in my branch.
Remove the source repository from the remote list, by using the Settings button.