But, from what I can see, the Payment_ID column matches to a value 67280309 for Reissued_from_payment_id. How do you related it to 33333 when the payment_id for that is 22222? I think you need to explain some more what it is that you expect to get from the data you have provided. Based just on the information in front of us, I don't see a solution that will be consistent from query to query.
Are you trying to find the previous reissued_from_payment_id in the ##second table? If so, can we guarantee the ordering of that column will always be what it is in the example (and yes, before anyone tells me, assuming I put an ORDER BY statement in, of course)? If that's what you're looking for, maybe there's a solution, but you need to explain in more detail.