It will depend on how the systems are connected. If SNA protocols are available, then the STRPASTHR command can be used. If TCP/IP is required, then your menu can execute a TELNET command instead. TELNET is most common nowadays.
Both commands allow you to supply the user ID which you can retrieve from the job attributes. Both also allow you to supply the password, which you will need to get from the user. The commands can be prompted so the user can type a password directly into the command. By sending user and password with the commands, you can avoid having the normal system signon panel from being displayed.