From here you get that in step 2 of ECDSA sign process, you use z, the Ln leftmost bits of e = HASH(message/transaction) in both the process of generating and verifing the signature.
I understand that in bitcoin transactions signature and verification you do almost the same algorithm.
You know that adress A has a transaction x to it that values in 1 BTC not spent.
You know also a transaction y1 from A with a certain signature and a certain value z1, as the algorithm in the link says.
Could you create a transaction y2 so that it sends the 1 BTC from A to adress B by creating it in a way that it had the same z1 (mentioned above) and consequently the same signature of y1? (since signature depends only on message (z), private key and the random value k)
This transaction y2 would be valid?