Use PAM to print the motd.

etc/pam.d/sshd-sysadmins

@@ -6,7 +6,8 @@ session	[success=ok ignore=ignore module_unknown=ignore default=bad]	pam_selinux
 session	required							pam_loginuid.so
 session	optional							pam_keyinit.so force revoke
 session	optional							pam_umask.so
-session	optional							pam_motd.so motd=/run/motd.dynamic # /etc/motd is handled by sshd.
+session	optional							pam_motd.so motd=/run/motd.dynamic
+session	optional							pam_motd.so noupdate
 session	required							pam_limits.so
 session	required							pam_env.so
 session	required							pam_env.so envfile=/etc/default/locale

etc/ssh/sshd_config

@@ -8,6 +8,7 @@ GSSAPIStrictAcceptorCheck	yes
 LoginGraceTime			30
 MaxStartups			5
 PermitRootLogin			prohibit-password
+PrintMotd			no
 StreamLocalBindUnlink		yes
 Subsystem			sftp	internal-sftp
 UsePAM				yes