I don't think there is any direct way to transfer session variable from one application to other, as session variable is created with browser object only. even both tabs from same browser has different session objects.
I think database may be the good way to share between two application. OR The basic idea is that you store SESSION parameters in a database table and different apps check if those SESSION values exist.
Below link may be useful for you
How to Share Session State Between Classic ASP and ASP.NET[
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