Apigateway Websocket - how to pass identity id to any routes when using IAM authorizer ?

In websocket api, when using IAM authorizer in $connect route with cognito identity pool, is there any way to get context variable information of identity id in other routes?

I thought I could certainly see identity id in other routes(lambda integration), but there were only source ip context information.

How can I know identity id(authenticated in $connect route) in other routes?