Copies of permits are filed in the CM's office. Each collector is responsible for obtaining permits related to their projects. Permits are filed by collector name and date issued.
Getting started on permitting? Be sure to check out the SPNCH wiki on permitting, which has researcher checklists etc.
https://spnhc.biowikifarm.net/wiki/Permitting
ALL Collectors regardless of taxon (this means plants and insects too!) planning on international collecting trips should consult the Access and Benefit-Sharing clearing house at the start of their research for permits. The Access and Benefit-Sharing Clearing House
USDA is the major agency you should be aware of for import. Check USDA for regulations. Generally, only federally noxious weeds, parasitic plants, or protected species require additional permits.
https://www.aphis.usda.gov/aphis/ourfocus/planthealth/import-information/permits/plants-and-plant-products-permits/plants-for-planting/CT_Plants4planting_faqs
Collectors absolutely NEED to have copies of their permits on them at all times when they are collecting! Permits can either be turned to CM at time of acquisition or during donation of specimens for archiving.