I was missing two tables, and found them based on this thread:
https://frontaccounting.com/punbb/viewtopic.php?id=7241
Below are the steps for anyone with basic knowledge like me.
1. Using phpMyAdmin or similar tool, identify the company prefixes. In this example I want to transfer the data from Company 0 to Company 1.
2. Using the RENAME feature under Operations, move the following tables to different names (delete might work but something could go wrong)
1_crm_contacts --> x1_crm_contacts
1_crm_persons --> x1_crm_persons
1_cust_branch --> x1_cust_branch
1_debtors_master --> x1_debtors_master
1_suppliers --> x1_suppliers
3. Use the COPY feature under Operations to bring the data from the original company to the new company:
0_crm_contacts --> 1_crm_contacts
0_crm_persons --> 1_crm_persons
0_cust_branch --> 1_cust_branch
0_debtors_master --> 1_debtors_master
0_suppliers --> 1_suppliers
That's it. Company 1 should now have all the contacts from Company 0.