You can terminate the employee in the current company and hire the person in the new company.
Otherwise, it is as Sven said, you need to use Management of Global Employment (MGE).
MGE: see links below
What is Global Employee Mgmt in SAP-HR ?
Management of Global Employees - SAP Library
Check if Concurrent Employment (CE) applies to your scenario. Of course here as per SAP, the need is that an employee may be assigned simultaneously to different positions within the same company.
CE vs MGE
Q:- Difference between Concurrent Employment an... | SCN
Concurrent Employment and Global Employment - ERP Human Capital Management - SCN Wiki
Concurrent Employment vs. Global Employment
CE:
Concurrent Employment - SAP Library
Concurrent Employment (CE) | SCN
Is SAP's Concurrent Employment right for you? | Insight Consulting Partners
Concurrent Employment – basics | SAP HR
As per some findings, it has been used without any issues for employment in different countries - see link below