Sending a trusted certificate to server

if what you meant is ssl client certificate that comes from clients and your f5 vserver does ssl termination:
vserver has separate ssl sessions in client and server side, so cant pass client certificate in ssl layer.
the workaround is vserver inserts client certificate data into custom http headers when forwarding http req to pool members.

here are some examples:

https://my.f5.com/manage/s/article/K95338243

https://clouddocs.f5.com/api/irules/X509__cert_fields.html