With BIG-IP F5 appliance, you can encrypt all traffic between client and back end server using the same SSL certificate and Key.
The client establishes three-way handshake and SSL connection with a Virtual Server IP address on F5 system. The F5 system then establishes three-way handshake and SSL connection with the server. In the later situation, F5 acts as a client to backend SSL servers.
In the Virtual Server, under Server profile (Server), choose default profile 'serverssl' for working with SSL backend servers.