in the elevator at noon today, I heard an unknown colleague saidy it was obvious that his manager was going to be replaced obviously in the elevator at noon today.

Obviously needs to be close to what it modifies. (I assume you mean the colleague was saying, "It's obvious that so-and-so is going to be replaced." (He isn't going to be replaced in the elevator.) Personally, I think the sentence works better without "obviously" because that is a difficult word to fit into a sentence. "It's obvious" or "it was obvious" sound better to me.

I thought back to all the replaced managers I know, and founI realized that when their former bosses leaved andft, they were replaced by their new bosses.

I changed it to show a cause and effect relationship because your whole text is about who does this and why. I think "realized" is better to describe active thinking than "found."

CommonUsually, all the managers in a department are replaced one by one by their new boss's former team members.

I think maybe the bosses don't trust in any strangers exceptthe bosses don't trust strangers. ¶
¶
I think maybe the bosses don't trust anyone except their former team members.¶
¶
I think maybe the bosses don't want to put their trust in anyone besides their former team members.

In your sentence "except" doesn't work because it means that those are the only strangers the bosses trust. The point is that the team members are not strangers.

So they take their former team members with them to new departments with them together.

Putting the managers and team members next to each other in the sentence reinforces what is happening and makes it clear for the reader.

But, whether their former team members are more competent is an issue that needs to be considered.

The comma after "But" shows that this is a totally new topic and creates a little pause, so the reader knows this is the final sentence of the narration after reaching the end of the sentence.

I heard an unknown colleague saidy that his manager was obviously going to be replaced obviously in the elevator at noon today.

I thought back to all the replaced managers I knoew and found that when their former bosses leaved andft they were replaced by their new bosses.

CommonUsually, all the managers in a department are replaced one by one by their new boss's former team members.

"Commonly" works too, I just think "usually" sounds more natural.

So they take their former team members to new departments with them togetherwith them to the new department.

But whether their former team members are more competent is an issue that needs to be considered.

You should connect this sentence with the last one, like "to the new department, but whether their...".