It is at best misguided to send Project Managers to Scrum Master training and make them Scrum Masters. Here are some reasons:
1. Your new Scrum team is already doubtful they actually have authority (“right to do work”) per the rules of Scrum. Your culture is not supportive of the idea, and every signal the team is getting from higher-ups is telling them to hedge their bets on Scrum as described around the web and in the Scrum Guide. The team will therefore ask the Scrum Master (previously: Project Manager) what they “should” do.
2. The Project Manager-turned-Scrum Master is going to have a hard time not telling the team what they “should” do…..
a. The Project Manager-turned-Scrum Master is probably an authority-seeking type of personality. That’s why they they were drawn to Project Manager role in the first place!
b. Even if the Project Manager-turned-Scrum Master comes back from Scrum Master training an enlightened and transformed creature, THE TEAM has no clue about this and is still projecting authority on the Project Manager-turned-Scrum Master. This pattern might persist for some time.
c. Even if the Project Manager-turned-Scrum Master comes back from Scrum Master training an enlightened and transformed creature, this new Scrum Master is clueless about executing in the role. This person has no experience.
All of this works against success with Scrum.
Usually, the Scrum Master is selected by the higher-ups. This is why the selected person is usually a PMP, or a Project Manager. (The Scrum Guide is silent on who chooses the Scrum Master.)
Here is a better approach:
1. Train everyone in a 2-day agile/Scrum class. Have the course delivered by your eventual coach.
2. During training, make sure the Scrum Master role is clearly explained. make sure it is explained from a servant-leadership point of view. Make it plain the Scrum Master identifies and removes impediments, and does drive schedule, cost, quality or features like a traditional Project Manager.
3. During the training, do some simulations of Scrum where someone can play the Scrum Master role. Offer the role to all the folks in the class and see who self-selects to give it a try.
4. Have the coach model the Scrum Master role when Sprints kick off. Make sure that the purpose of the coach occupying the Scrum Master role is to mentor this new Scrum Master. As soon as possible and without delay, install this new Scrum Master and get the coach OUT of the Scrum Master role.
5. Have the coach keep mentoring and guiding this new self-selcted Scrum Master in the art of occupying the role.
Summary
Instead of having the higher-ups select the Scrum Master, explain the nature of the nature of the role and see who shows up. Realize that putting a Project Manager in the role is probably not a good idea. Project Managers are typically authority-seeking and are great candidates for the Product Owner role.