it depends on your relation with director.

in many cases, if you are performing good have good feedback good relation with colleagues and director you can be offered better incentive to continue in same post.

however your case is different as you are in university there could be many students used for same post if i am not mistaken.

sharing the letter should be done carefully after consultation with your seniors/family members/trusted friends as it can have both positive or negative impact too.

on the negative side the director may develop mistrust, see you as unreliable etc.