How to use WP account on third party module

Our client has an existing website which runs on wordpress. They want a separate module which will be made by us. This module won't be made as a Wordpress plugin and will therefore be hosted on a different server. The WP user can see this module after he is logged in. To see the module it will be loaded by an IFrame.

Is it possible to use the WP account of the user to authenticate on this module (for example with OAuth)? If so, how do we do this? Is an IFrame the only sollution to see our module on their wordpress website?