User is a member of AD "linux_admin" group. When I run 'id', it
doesn't show he is member.
By sudo log, do you mean sudo debug log ? I have following there:
sudo sudo_getgrnam: group linux_admin  -> gid 10001  (cached)
sudo sudo_get_gidlist: looking up group IDs for testadmin
sudo user_in_group: user testadmin NOT in group linux_admin