I try to move email from mailbox's gmail to another one, Just curious that UID of each email will change when move to new mailbox ?
Yes of course the UID is changed when you do move operation.
the new UID for that mail will be the next UID from the destination folder.
(i.e if the last mail UID of the destination folder is : 9332 , 
then the UID of the move  email   will be 9333) 
Note: UID is changed but the Message-Id will not be changed during any operation on that mail)
About IMAP UID with imaplib