Including Packing Slip with Fulfillment Notification?

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We're using a 3PL so when orders go through our 3PL is notified via the Custom Fulfillment Notification function. My question is around including the Packing Slip with that message. Or another automated message? Is it possible?

(Actually, if the entire default notification/email message could be swapped with the packing slip, that would be great. Not a coder, but I tried to copy the liquid code from the Packing Slip to see if that would work in the code of the notification, but alas, no.)