Business partner migration is little tricky. We are using Rapid Deployment solutions from SAP for S4HANA to migrate data. However For business partners migration please take look at this BAPI - RFC_CVI_EI_INBOUND_MAIN
This function has pretty much has almost all of the businesspartner/customer/vendor fields
For your particular partner functions case, there is segment in the above mentioned BP that you can use.
P.S. - If you decide use this function module please share us your experience.
Regards
Krishna