Recently I got asked a small but unobvious branching question. Suppose you have a folder named FolderName, and for some reason you have renamed it to NewFolderName. All is well, but now you decided you want to create a branch from that folder, and to branch from the version prior to renaming.
Due to the reasons detailed in my older post, you will not be able to use branching UI for the operation. The only way to achieve that is to use tf command-line client branch command where you will explicitly specify version you branch from and the folder name at that revision
tf branch /Project/FolderName /Project/Branch /version:C123
Typical mistake people make is to use current item name, NewFolderName instead of the name that existed in the past(i.e. FolderName at the time of changeset 123).