Pass exposed filters values from one view to another view
Option 1: Views Global Filter. I've never used it but it sounds like a good but very heavy solution.

Option 2: Create the url for the second view dynamically with jQuery every time the exposed filters are changed. If you disable Ajax in the second view, you can see the url change and then use that as basis. The url will still work if you switch on Ajax again.

Option 3: Tokenise the exposed filters and create the link like option 2 in the header or footer.  There seems to be a couple of modules / sandboxes that could help.

I'd probably pick option 2 but of course, there are probably other solutions like your session variable and some views hook.