Sorry for keeping silence.
Both the library are having LTO6 tape drives and the tape are barcoded.
Then this behavior is unexpected. Generally, you can share the same tape between tape libraries without any issues. Tape should be exported from once device via VBR console and then loaded to another device. You should see this tape under second library > media > online.
As simple media pool is tied to tape library and once library is removed, the pool gets offline along with all the tapes. What is procedure to restore from these tape? I hope it is not to import the media in new library, as it will take 4 to 6 hours per tape if it is LTO6?
Should be easy. Just change the tape device in media pool properties and remove the old one. Tape media and catalogue info should remain untouched. Take a look at this article for more details