I am assuming that those same shared resources that User1 has access to might not have permissions for User2.
What I recommend is going to this shared resources and adding permissions for User2. This should fix the problem which is a very common one that all people (me) do it some time (all the time for me).
Some ideas might be adding both users to a same group that has access to this same resources.
To add for example user "user2" to group "user1" you might use something like this:
useradd -aG user1 user2 - Where user1 is the group name and user2 is the user name.
Remember that when using adminstrative commands, you need to prefix them with the command sudo. For example, the above would be
sudo useradd -aG user1 user2
Another tip to help and check quickly would be to allow complete access. This is just a test to see if the problem is permissions. For example if you external unit is mounting in
/media/My Passport 1 you would do something like this
sudo chmod 777 "/media/My Passport 1". Why the double quotes you may ask. this is because My Passport 1 has spaces between it. This is a quick and dirty way but other ways like
/media/My\ Passport\ 1 also exist.
I also recommend opening the GUI tool "Disk utility" and changing the label from "My Passport 1" to a one word name, like "Stuff" or "Photos". Open the DASH many and type
disk. It should bring an icon called Disk Utility. Open it and from there you should find your drive, change the label from the one you have to a shorter, easier one.