This is information regarding transferring visa and/or visa extension in Chiangmai Immigration office.
After having applied a new passport, I enter the Kingdom with both former and new passport. The papers you need are
1. Form for visa transfer. You can download the form Internet, or request it at the office counter.
2. From your new passport, you need to photocopy the ID page, entry stamp. I included the backside of departure card with the entry stamp.
3. From your old passport, you need to photocopy the ID page, and "every page of your current visa and extension." This is that it means. I am staying in the Kingdom on an extension applied this March and it was based on a visa I used in June 2016. Therefore, I need to photocopy every page from June 2016 to this year.
4. Visa transfer is free.
Bonus point: According immigration officer, you can do TM30 reporting regardless you have transfer your visa or not.
TLDR : Answer Summary
This post provides detailed information on the process of transferring a visa or extending a visa at the Chiang Mai Immigration Office. To transfer a visa to a new passport, the applicant needs to submit a visa transfer form, photocopies of the ID page, entry stamp, and all pages of the current visa and extension from the old passport. Additionally, the transfer service is free of charge. Comments clarify that this process applies only to extensions of stay, not actual visa transfers.