Changing the Product Updates Category Drop Down

The problem that needs to be solved is that if you move an idea from one product to another the drop down list of categories does not update to that of the new product. I know that this is not a big deal but it would be nice to change

ex. I have Idea A and i am categorizing it. I add some tags and click on the category drop down to apply one. I then realize that This should be moved from Product One to Product Two. I then move the idea to Product Two. This updates the statuses and the transition buttons. I then move to the categories to give the idea one. If you click on the field right now the drop down will be that of the categories in Product One. If you search a category in Product Two it shows up so the program knows it has access but will not change the drop down. The only way to fix it is to reload the page, but if you are filtering to one product the idea will disappear. 

Thank you for the consideration.