VSTS Kanban how to incorporate Test team work

I'm looking for suggestions regarding how to incorporate Test team work to a VSTS Kanban board for continuous software development on a web application.

What makes the most sense to us initially is to implement this as two boards running concurrently such that for each Dev sprint our Test team is operating off a backlog created by the previous sprint. For example:

DEV BOARD (current sprint)
+-------------+--------+---------------+---------------+
| DEV Backlog | Active | Code Complete | Peer Reviewed |
+-------------+--------+---------------+---------------+
| item7       |        |               |               |
|             | item6  |               |               |
|             |        | item5         |               |
|             |        |               | item4         |
+-------------+--------+---------------+---------------+
                                             /
                                            /
         _________________-----------------/
        /
       /
TEST BOARD (next sprint)
+-------------+--------+---------------+---------------+
|TEST Backlog | Active | Test Complete |   Deployed    |
+-------------+--------+---------------+---------------+
| item4       |        |               |               |
|             |        |               |               |
|             |        |               |               |
|             |        |               |               |
+-------------+--------+---------------+---------------+

But it's not clear how to implement this in VSTS. Do we need to create two teams? A Dev Team & a Test Team - with their own boards - and if we do, how then do we get the workflow configured such that what is completed in the current dev sprint feeds/fills the backlog for the next Test team sprint?

Suggestions appreciated and welcomed! Thanks