I'm not quite sure what you're looking at. Do you mean Waverly, NY? Pennsy never had a line there. It was the Erie, DL&W and LV that ran thru Waverly back in the day. The nearest Pennsy line was the Elmira branch but that's quite some distance away.
No, he's talking about Waverly NJ, just N of Elizabeth. From the map it looks like they had planned some branches from here; one goes straight across to Jersey City and Bay Ridge! So would that be the "transfer"?
Triumph V doesn't mention "Waverly Transfer" by name, but it mentions a "large freight transfer facility" built at Waverly 1904-1905. Waverly Yard lay just to the south (railroad west!) of Waverly proper, so this is probably "Waverly Transfer".
Waverly Transfer may refer to the LVRR interchange track going up into the Oak Island Eastbound Recieving yard of the Lehigh Valley. The interchange switch began just east of the Bayline spur at WA-2 off the PRR's Greenville branch. Prior to Conrail the Valley would recieve 20 - 30 loads a day off the PRR / PC at this location.