Can I generate private key from the last public key using puttygen?

You cannot generate private key from public key but you can generate public key from the private key using puttygen. As @alfasin mentioned if you could generate the private key from public key then RSA would be useless and this would make you vulnerable to attack.FYI the public key is used for encryption and private key is used for decryption. this wikipedia page will help you better understand the reason.

If you were able to do that, RSA would have been vulnerable to a "puttygen" attack...