Yes, 1 window with 2 tasks on both sides.
Thank you for your effort!

“Save to Batch” button is nice!
Please also revert the double-click (for single item) and “Edit” button (for multiple items). It’s necessary, since the window is 2-task. So the left board changes only when the user really wants to.
Batch dialogs are big enough for this button.

By the way, is “Close” button necessary (even for touch screens)?

“Select from Batch List” menu is not really the solution for “Search Favorites”, right?
(If it is, I hope I can set to show/hide any item.)