Assume this feature is about the UI needed for assignment only, as we already have item and holding to location assignment on the back end.
Wireframes for assignment can be found here: https://drive.google.com/drive/folders/1xUVa2Gg3TEZxFuBqYjsRt4Jl5tTSPp4g
UX is working on proper mockups as part of
The general idea is that users that know the location code or name should be able to type either the location code or name into a textbox and the system should auto-complete. When the name or code is unknown, they can launch a location browse popup.