She is only 17, but my order says support ends when she turns 18 or graduates HS, whichever occurs first. I pay half on the first and half on the 15th. Can I prorate my last payment through 6/3 or do I have to pay through 6/15 or 6/30?

It would depend upon the exact wording of the support order. Chances are it says "... shall pay so much per month, payable on the 1st and 15th of each month, until the child turns 18 or graduates high school, whichever occurs first". If it is something like that, you are probably obligated to pay for June (the whole month), although the payment is split in two. Since she won't have graduated by June 1, you will owe for the entire month. That's my guess based upon the probable wording as set out above.

You are going to begrudge your daughter a half month of support? Shame on you! You should be happy and proud that she is graduating early.

But no, usually support ends in the month AFTER the ending event occurs.