This will not work as expected if both companies are still using skype.
Ideally what you want is to be full Teams mode
To configure external access and users being able to talk between different 365 Tenants
Log into Tenant 1 365 Admin console / Teams section / org Wide section / External Access
Enable External access ( Teams ) – Skype optional if still using Skype. But be aware the messages from teams instead will go to Skype .
If your tenants are on full teams mode you do not need the first two options ticked
If an external users sends a message to a user in islands mode, it’s always going to Skype!
Add on tenant 1 tenant 2 as allowed domain and you will do the same vice-versa
on tenant 2 you will add the domain of tenant 1 as allowed external access
This change is not immediate applied , be patient!