Although Pumbush already said his, it might not be clear enough so I will say it as well so learners are not mislead: one of the "correct" answers given is: "לשניהן יש יום הולדת".
There is no such word as לשניהן! It should have been: לשתיהן.
yesh le-shneihém yom hulédet
Should also accept יש יום הולדת לשניהם
Why can't you say יש לשניהם as well??
The Hebrew sentence above is wrong. is should be Shteihen or Shneihem. There isn't such word Sneihen.
So you are right.
I think it should also accept יומולדת, as it's very widely used.
Sometimes used but not correct Hebrew. I've mostly seen it on greeting cards trying to be hip, but no one in my personal circle says this.