Actually DoubleLung, that may not be true.
Here is the relevant PA statute:
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Pennsylvania Statutes
TITLE 34 GAME (Pa.C.S.A.)
CHAPTER 23 HUNTING AND FURTAKING
SUBCHAPTER A. GENERAL PROVISIONS

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34 Pa.C.S.A. § 2304. Ownership of carcass of game or wildlife

(a) General rule. — The carcass of game or wildlife lawfully
killed or taken shall be the property of the person who inflicts
a mortal wound which enables that person to take possession of
the carcass.

(b) Officer not to arbitrate disputes. — No officer whose duty
it is to enforce this title shall be called upon to arbitrate any
dispute concerning the ownership of game or wildlife or to
testify concerning any such dispute.

1986, July 8, P.L. 442, No. 93, § 1, effective July 1,
1987.
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I don't know how PA courts have interpreted this statute, but I interpret it as following the "mortal wounding" rule. If he made a shot that would have enabled him to take possession of the carcass (a double lung shot would undeniably have done that), then the animal is his property. It doesn't require immediate possession, only that the shot would "enable that person to take possession." The statute is not written very well though, so who knows how it would be interpreted.