1 has to get the extension of stay. Then you need proof that you are legally married translated and certified by the Thai foreign ministry. Then the partner can get an extension of stay without any financial requirements.
2.19 In the case of being a family member
of a Thai resident (applicable only to
parents, spouse, children, adopted
children, or spouse’s children):
Each permission shall be granted for no more
than one year.
(1) The alien must have been granted a nonimmigrant visa (NONIM).
(2) The alien must have proof of relationship.
(3) In the case of spouse, the relationship must be de jure and de facto: or
(4) In the case of children, adopted children, or spouse’s children, said children, adopted
children, or spouse's children must not be married, must live with the alien as part of the
family, and must not be over 20 years of age except in case of the person hereof is of illness
or disability and cannot live without support of father or mother: or
(5) In the case of parents, the father or mother must be 50 years of age or over.