Export wordpress authorization credentials

I am building a Wordpress site where I temporarily redirect the user to my own third-party application as an additional service.

I am wondering if their credentials can be carried over to my third-party application. So that if they are logged in to the Wordpress site, then when they are redirected to my third-party application, it will get that information as well as the account information of the user.

I just started tackling this problem, and been looking around in Wordpress, and haven't tried anything concrete yet.

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