No, to be able to perform that the attacker must have the private key associated with the certificate of the website (private key used to generate the public key in the certificate). The client will send a challenge to the website during the SSL handshake and if it does not come back signed with the private key of the website it knows it is not talking to the website in it is trying to talk to.
The attacker cannot generate a different key-pair because the client has a CA certificate (in the browser or as part of the OS) that sings the website's certificate. The certificate signed by the CA relates the domain of the website to a public key and only the private key of that specific domain (i.e. that public key) would be able to sign the challenge text correctly.
On the other hand, if the attacker can get hold of the private key of the website (to achieve which he would likely need to copy it from the website's servers) then he would be able to perform HTTPS to the client.
Yet, this is not an SSLstrip attack anymore, this would be a plain compromised certificate. And, if the website discovers the compromise, will likely add its certificate to a database of compromised certificates. For example the OSCP database which several browsers will check (of course the attack may be ale to spoof the OSCP request).
Another option is to fool the client (thanks @crovers). If and attacker can make the client to accept a new root CA certificate, he can sign the domain with his own CA and provide that as a certificate instead of the real one.
This again is not SSLstrip, this is a form of phishing the user into installing bogus CA certificates.