Need to get password after login

I know, I know, passwords should always be hashed and not be reversible but I need to bridge EE into another system so I need to get the users password.

This is only temporary because the other system has a one time token build in which is not yet finished.

Basically what I need is for an icon inside an EE members page when clicked logs the existing user into the other system with the same EE username and password. Its obvious that I don’t want to use a temp password on the other system, the username and password should be the same as the Expression Engine Member user. The problem to achieve this is that passwords are hashed, (correctly so).

So my idea is the following, get the password after the user logs in, from the POST form or some other way with PHP??? This is basically my question. How to get this. Once I get this for security purposes I will encrypt this in a session or in memory with PHP and I only need to use it one time because I need to pass the login into the other system when the users clicks the access icon. Then its deleted.

My question is if there is a variable or some other way to get the password used by the user that logs in to EE?