What you show us is not the stern but the bow of the Spanker as far I can see.
There are more ways to Rome
![:) :)](/media/kunena/emoticons/smile.png)
but you can repair this with two part epoxy resin mixed with wood dust from the sanding machine. Make it as thick as peanut butter.
But first you've to scrape and sand away all paint, and remove all rotten wood so only clean healthy wood remains.
Hopefully you end up with a boat after removing the rotten wood (could not resist the joke).
But if, then you could fill up the gap with the epoxy / wood dust mixture.
After curing this will sand quite well.
Eventually you can make it smoother with epoxy putty.
If you want to go for 100% sure leak free you can think about laminating glassfibre over the bow though this is not easy (need to be airbubble free else better don't laminate).
There is quite some information about working with wood and epoxy on the internet, e.g. the Gougeon brothers have written a book about it which is free available in PDF.
Freek