Authorization across subdomains

Question

I have a case:

• In theta.smatyx.com: Set 1 domain-match cookie (with domain: .smatyx.com), with value of 1 short-lived jwt, signed with theta.smatyx.com).
• In mylong.smatyx.com: Redirect to page mylong.smatyx.com, at this time the above short-lived cookie is still kept. mylong.smatyx.com will request to login, based on the above short-lived cookie. The server returns the session cookie. There are 2 cases: session cookie will be cleared or will be used for mylong.smatyx...

I have used http://localhost:8080 for one service and http://localhost:8081 for another.

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How can I retrieve UserID based on the session cookie and shared between subdomains?