Remember, Akeeba Backup makes exact clones of your site, including all files and database contents. You cannot use it to transfer content (such as articles and modules) between Joomla! versions. Therefore, the only instructions I can give you is how to restore your backup and an overview of how to upgrade from Joomla! 3.10 to 4.4, and from Joomla! 4.4 to 5.1.
First, you will have to restore the backup of your old site to an empty server with PHP 7.4 (you must NOT have Joomla installed on it at this point).
Go to the backend of your site.
Set the site off-line in Joomla's Global Configuration.
Then, make sure that Joomla! and all of its extensions are updated.
Disable all third party extensions except for Akeeba Backup.
Uninstall any extensions which do not have a Joomla! 4 version.
⚠️ IMPORTANT! Your site's template is also an extension. You will probably have to select the default template (Protostar) before removing your site's template.
Take a backup.
Go to Components, Joomla! Update and click on Options.
Set Update Channel to Joomla Next and click on Save & Close.
You will see that Joomla! 4.4 is available. If not, click again on Check for Updates.
Ignore any messages from Joomla! about any of the Akeeba Backup plugins; they are false and misleading.
Proceed with the update to Joomla! 4.4.
After the update, go to the backend of your site and click on Components, Akeeba Backup.
Follow the instructions on your screen to install Akeeba Backup 9, migrate your backups and backup settings, and uninstall Akeeba Backup 8.
Note: Akeeba Backup 9 is currently compatible with both Joomla! 4.4 and Joomla! 5.1 on PHP versions 7.4 and later. You don't have to bother with Akeeba Backup after this update.
Take a backup.
Update all third party extensions to their Joomla! 4 versions.
Uninstall any third party extensions which do not have a Joomla! 5 version.
You might need to select a different template for your site, e.g. the default Joomla! 4/5 template, Cassiopeia.
Upgrade your PHP version to 8.1, following your host's instructions.
Go to System, Update, Joomla, and click on Options.
Set the Update Channel to Joomla Next, and click on Save & Close.
You will now see that Joomla! 5.1 is available. If not, click on Check for Updates.
Proceed with the update to Joomla! 5.
After the update, go to the backend of your site.
Take a backup.
Update all third party extensions to their Joomla! 5 versions.
Assuming all of your extensions support PHP 8.3, you can now upgrade your PHP version to 8.3.
Set the site on-line in Joomla's Global Configuration.
Most likely you need to rework your site (e.g. setting up your template, changing modules and plugins, etc) to make it look and function like it did on Joomla! 3.
Nicholas K. Dionysopoulos
Lead Developer and Director
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Please keep in mind my timezone and cultural differences when reading my replies. Thank you!