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To update your license key:
Go to your Bitbucket: click Administration ⚙ → Manage apps → Snippets for Bitbucket
Click Edit 📝, located to the right of the License key field.
Enter your key, click Update, and you are done!
See Atlassian documentation for more details on switching from Server to Data Center Bitbucket version.
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This case does not differ significantly from the process described in Bitbucket Server to Data Center (in-place). Once you migrate from one instance to another, all hook settings are also migrated. You only need to update the Snippets for Bitbucket license when migrating to a different instance type.
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If you are interested in a cloud version, contact us and let us know!