In the SSL vhost that handles the request, you can try something like this -- but it is quite specific to the source and target URLs:
RewriteEngine on
RewriteCond %{HTTP_HOST} =subdomain.domain.com
RewriteCond %{QUERY_STRING} ^a=([^&]+)&b=([^&]+)
RewriteRule ^/project/page.jsp$ /%1/%2 [PT,E=CHANGEHOST:1]
RequestHeader set Host othersubdomain.domain.com env=CHANGEHOST
If you can just redirect, you would skip the last line and just build a URL in the RewriteRule and drop the current flags for [L]