They are only providing the list of document for marriage extension in Thai also. They used to provide the list in Thai and English but someone got the bright idea to provide them in Thai only now.
You need to transfer an extension of stay if you have one but you do not transfer visas (done free at immigration in one visit). Just use in the old passport as others have said. Present both passports when you enter the Kingdom.
If you a planning a move to another province go and get a new savings account at a local branch close to the immigration office before you move. This will also give you time to season the funds in the new, local account. Some offices require letters same or previous day only and a local branch will become a necessity.
Chris Isherwood Something else I just thought of. Is your license the five year license with a plastic card and certificate or is it a two year temporary license? If temporary that is also tied to the current school and not valid at any other school. If you don't have the five year license then you will need to get a new two year temporary based on the new school and you just wasted two years out of six years you can get temporary licenses before enrolling in a Master's of Education program or otherwise qualifying for the five year license (such as having a teaching credential from another country that is recognized by Khurusapha).
Ron Angel They have two branches that accept retail deposits in Thailand. One at corner of Asoke and Sukhumvit and one on Silom. Currently minimum to open a new savings account is 1 million baht.