Hi Nandhi , To send Logs to remote syslog servers , accomplished by 2 methods :
Syslogng utility which runs over Linux :
in this method you will face some difficulties to filter / or send specific log messages such as your scenario here of "Audit Logs " by Gui.
you can send Audit logs by configuring syslog-ng but this can be done only from CLI , to do that follow this article https://my.f5.com/manage/s/article/K56602501 , it just simple modification using some simple linux commands.
High speed logging ( HSL ) and this run over TMOS :