As a scientific diver, you must be affiliated under the auspices of a program. Your home institution holds your dive related paperwork as long as you maintain diver status there. If you transfer locations (i.e. you began a Ph.D program or accepted a long term position elsewhere) and will be diving under a different organization, your records will need to be sent by the DSO to your new institution's DSO.
If you are diving through another program temporarily but intend to remain an active MLML diver, you need a letter of reciprocity (LOR) sent by MLML's DSO to the new institution's DSO. (i.e. you got a summer internship helping a researcher on Catalina but plan to come back to finish your degree).