Getting Related Team Information from Private Channel in SPFx MS Teams App

Just two weeks ago during MS Ignite Microsoft Teams team has announced Private channels - one of the most asked features.
So, a bit of technical details. Each private channel is a separate SharePoint site collection with a unique site template and no group assigned.
We can discuss a lot if it's good decision or not.
But in this post I want to focus on a specific problem I experienced while developing SPFx solution for MS Teams.