hii Aswanth Balagurusamy,
for both apps your database is same means your user table is same , now you can make a attribute (example is_login) so when someone logged in App A then you can change value of is_login attribute/column to true in Table and on logout make it again false
so in App B check if user is_login true means it is logged in in App A so in App B you can set users session programatically and redirect to dashboard else redirect to login page.
hope this will help you.
Thanks & Regards
Sanjay Kushwah