Yes, you can use the SAML module for this, but you do have to have an Identity provider(e.g. ADFS) in your application landscape.
What do you exactly mean with "this"?
to login automatically to another Mendix application using the current username and password. Username and password should be checked.
For the SAML Module it works roughly like below:
You should direct a user to a specific entry point in your web application where the user its (login) request will be handled. For example 'myapp.mendixcloud.com/SSO/ where SSO is a server side request handler entry for the SAML Module.
If you want to switch from one Mendix app to another Mendix app you could also use a webservervice and deeplink for that. To the webservice you supply the user that wants to log in. The webservice returns a deeplink which can be used by the other Mendix app to redirect the user.
Regards,
Ronald