How to POST data to specific page after APM authentication?

Do you need the data to be sent via POST only ? If so then you would need an iRule. Add the General Purpose - iRule Event to your policy with a name lets say "Event1"

Now add an iRule to your virtual server for Event1 and then use SIDEBAND to POST out your data.

when CLIENT_ACCEPTED {
        ACCESS::restrict_irule_events disable
}
when ACCESS_POLICY_AGENT_EVENT {
        if { [ACCESS::policy agent_id] == "Event1" } {
            SIDEBAND::connect -destination ....
            SIDEBAND::send "POST ..... "
        }
}

If you are just trying this to log data, instead of POST you could use the policy General Purpose - Logging to send out data to a remote log server.