“Please join me in congratulating him on his new position.”

You have given one of your employees a promotion. You're writing an email to everyone in your division of the company to announce this and congratulate him. After describing his accomplishments and strengths, you finish your message with this line.

Please join me in congratulating him on his new position.

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Please join me in (doing something)

In very formal writing or speech, you can use this phrase to invite people to celebrate something or feel something together with you. Here are some common examples:

Please join me in congratulating Penny and Esteban on the birth of their first child.

Please join me in welcoming Marcus to the team.

Please join me in wishing Estelle and her family good luck on their move to Australia.

"Please join me in ___ing" is often used in formal business communications.

congratulate (someone) on (an accomplishment or lucky chance)

What does it mean to "congratulate" someone? Basically, it means to tell someone "Congratulations". This is just a nice word that you say to a person when something great has happened to them. People congratulate each other on events like:

getting engaged

getting a job

winning a game

To express the reason for congratulating someone, use the phrase "congratulate (someone) on ___":

Aren't you going to congratulate him on winning?

Congratulations on your new house!

a position

In business, a person's "position" is his or her job or job title:

My current position is Assistant Director of Sales.

That position has been open for a few months now. I wonder when they're going to hire someone.

The word "position" sounds classier and a little more formal than "job" or "job title".