I have encountered some cases like you. You should read the rules carefully as they may accept post hastag or share their social sites. If unfortunately, you should take a week off wait their post
Yeah, if their facebook page is not updated and you shared already all their post I think just try to make your own post about that project, I know some campaign are allowing this to their participants. I think if one facebook page is not updated maybe there is something wrong on their marketing team, or they are really not working well on their project.