Multi tenant and Teams collaboration

A customer of ours have bought a company that also has its own 365 tenant.

For now they are not able to merge the tenants due to some contracts with the bought up company's CSP.

The CEO in the company want to be able to collaborate with the new company (mostly in Teams) without doing the tenant switching. 

Is this possible with the cross tenant sync, and use the already existing teams and channels (they have no shared channels)?

I have set up cross tenant sync, and sharing a Shared Channel from "Tenant B" to a user in "Tenant A" works without having to do the tenant switch.

If I try to share a Team, or a Private/Public Channel, the Team/Channel will not show in Teams of the user in "Tenant A", unless the user switch to "Tenant B". Is this by design, or is it possible to do?