How to migrate mails from GMAIL to Office365 Exchange

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I have a customer with a mail domain running with Google Mail called DOMAIN.DK.
All of these users access their mails through web mail.
My customer wants to migrate to Office365 Exchange.
Is there a way to extract all users mailbox from GMAIL and upload it to Office365 directly without having to sync the mailboxes to a pc with Outlook and make pst files from here?

Is it possible to access the old gmails after migrating to Office365 through another domain name?
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Operations Director
Nice cost effective solution i have used before:

This will allow you to import all mail from Gmail into 365, full support in the event you need it.

i have also used this tool:

Take a look at both and if you have any questions feel free to ask. if you are not looking to pay for a tool i'm afraid its a manual process
The following article gives a good overview of the migration proccess:
How to migrate from an IMAP server to Office 365
When it comes to the manual migration - you don't have to use Outlook to export mailbox data. You can go to Google Account > Data & personalization > Download your data and choose what you need to be exported.

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