1964 Kennedy Half Dollar Error

This Kennedy half dollar error is one of 2 that my father got directly from the bank when the coins were first released.
The Teller at the bank apologized to my father for passing coins in such poor condition.
She offered to take them back and he informed the Teller he wanted to keep them. He held the coins in his pocket for some time prior to putting them away (thinking they may be worth something some day).
My father has since passed this one on to me and I have shown it to many people and NO One has ever seen one like it.
The other is even more rare - - It is missing the back of the head from the blank being under-filled just as this one is (they do not appear to be cracked, clipped, or chipped - - the look to be under-filled planchets prior to striking).
I placed it in a keeper that my friend gave me and I only have these photos at this time (its hard to get good ones with the reflection).
Question to the forum:
Can I trust sending it in to be graded?
Has anyone ever seen one like it?
My father still tells the story today and I'd love to let him know what I find.
Thanks,
snscomp