The actual URL address (looks like a long string of numbers and letters) of a list should never be used, this link expires at the end of each year and will need to be manually updated.
For linking, the URL of the module page on the MyReadingList page is persistent. Linking to the module via the tool in Blackboard is also persistent – where the course name doesn’t match, a list can be linked manually via the tool in Blackboard as well and this is also persistent.