In inventory management is a bin nothing else than a text for a specific storage location of a material.
It is pure information and will be shown next to the location in MMBE transaction, also it is possible to select record for a physical inventory based on that information. But this is all what it does.
If you have entered BINAAA in that field in the material master storage location view then you just change it in the material master to BINBBB if you have moved your material physically. But in SAP itself you will not have any movement as all material still stays in the same storage location.
This answer is purely on the fact that you have chosen the MM tag. If you have WM then the answer would be completely different, but then your question should have been asked under the Logistics Execution tag, which is the same name as the menu where you find the WM related transactions in your system.
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