Hi,
You could utilize the feature of migrate printer under print management to accomplish the printer server migration.
The basic steps are followed as below, bit different than you requested to change IP and server name of the new printer server from print2 to Tprint 1 in case of some unknow risks:
(1) Make sure that the existing print drivers are compatible on the target server (Tprint2). For Tprint1, please ensure that all print drivers are up to latest version and use universal print drivers when possible as well.
(2) Install the print and document services role on (Tprint2) with different ip address from Tprint1.
(3) Export the queues, the drivers, the print objects, and security settings from the source server into a printer data file and then import to Tprint 2.
(4) Publish printers to client computers from (Tprint2), the client computer will get printers from two servers and you could verify if printers work well from Tprint2 Server.
(5) If the migration works well, then we can unpublish printers from Tprint1. And users will get only 1 group deployed printers from (Tprint2) printer server.
(6) Disable printer server computer account or unpublish Tprint1 printer server from AD domain.
Kindly go through the reference Video and document before start the migration:
Step-by-Step: Migrating Print Servers from Windows Server 2008 to Windows Server 2012
https://video2.skills-academy.com/zh-cn/archive/blogs/canitpro/step-by-step-migrating-print-servers-from-windows-server-2008-to-windows-server-2012
Migrate Printers from Windows Server 2008 R2 to Windows Server 2012 R2 (This also listed out some checks before and after the migration)
Please note: Information posted in the given link is hosted by a third party. Microsoft does not guarantee the accuracy and effectiveness of information.
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Thanks,
Jenny