My personal emails were hosted by OVH in their Exchange services since 2003 and this service didn't really evolve that much for the price I have to pay every month.
So I decided to move from OVH to Office 365 and this has been my first time so I documented it, it can maybe be useful for someone.
You need to have the Office 365 admin website : https://aka.ms/admincenter
you also need to have your OVH manager webpage opened : https://www.ovh.com/manager
First in the Office 365 admincenter page, go to Settings / Domains and click Add Domain
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Add you domain in the form domain.com
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Then follow the process and chose the option suitable your usage.
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In the OVH manager, create the TXT entry as requested on the Office 65 admincenter
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Chose TXT field
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Enter the values you got in the Office 365 admincenter
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Once it's done go back to the Office 365 admincenter and click on more option
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I chose the second option because I wanted to check it worked, and it did !
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I didn't need the Skype for Business and Device Management as I just need the email services
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I chose to import the DNS entries from OVH
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Next these are the DNS informations needed to be changed in OVH
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I had to modify in text mode
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and change the DNS servers by the Microsoft ones
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As I had DNS Sec enable, I have this error that stopped me to continue, once disabled I had to wait 6 hours before being able to move on and finish the process.
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Here you go. Now you just need to create a new user with the right UPN to enable the mailbox.