How can I support .aspxauth session cookie between website and virtual application?

We have our .net web site and a third-party web application that acts as a virtual application from the web site. I was instructed to maintain session time between the website and the third-party application. that is, while the user is active in a third-party application, the session remains alive, so when they return to the website, even if it expires after 20 minutes, their session is still active. We use authentication on the website and in the session management application, and from what I read, I should be able to do this through the settings in the web configuration. I updated the authentication section of both webconfig files with

I mainly work with www.mydomain.com and www.mydomain.com/app/

    <authentication mode="Forms">
        <forms
           name=".ASPXFORMSAUTH"
           loginUrl="home.aspx"
           enableCrossAppRedirects="true"
           slidingExpiration="true"
           path="/"
           domain=".infinedi.net">
        </forms>

    </authentication>
    <machineKey
          validationKey="BDEA0BE471E4E2C24E5A9552AF232C3E7BF584DBEEAA1262CEE78CB5126FBBBE9E8007DB5ED8357FEE5C2C5B6FF3FC7D34C7CEA54DE3790560FCDEBF44415804"
          decryptionKey="2E31C984223964655C203E3A91AF139B1AE0A964F1475E204E6AACE62840EAB0"
          validation="SHA1"
          decryption="AES"
          />

. , , , .ASPXFORMSAUTH, , , , - . webconfig , ?