Biologically when a cell in invaded by foreign organism who inserts it’s DNA and the cell now spits out copies of the foreign genome that’s often a viral infection. From that perspective it’s arguably the sperm that’s preserved and using the eggs cellular machinery. In either case calling it the same organism is stretching the definition of same well past its breaking point.

Like you can apply the word “same” if you want, but what’s actually happening is isn’t a simple continuation of the original organism any more than a clone is the same organism and at least that’s more closely related genetically.