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In one of my internal projects, we had to migrate the contents from MOSS 2007 with fab40 templates to SharePoint 2013. You can also consider following the same steps, which is suggested by one of my colleagues.

A few changes in the steps in order to use the fab40 templates.

https://www.winwire.net/moss-2007-to-sharepoint-2013-migration-using-database-attach-method/

You can download the fab40 templates form the below link
https://drive.google.com/folderview?id=0B-YJgT3wyeZdWFJISzFqcVQyQVU&usp=sharing

We need to perform these sequential database-attach upgrades from MOSS 2007 to SharePoint 2010 and then to SharePoint 2013. And you intend to use the fab40 templates for SharePoint 2013.
After the step, attach restored database to the newly created web application in SharePoint 2010, you need to install all the required fab40 WSP.

Adding the solution

• Add-SPSolution “c:\Solutionname.wsp”

Deploy the solution

• Install-SPSolution -Identity Solutionname.wsp -GACDeployment
Follow the remaining steps from the above link.
Similarly, to migrate the content from SharePoint 2010 to SharePoint 2013, follow the same steps until you attach the restored database to the newly created web application in SharePoint 2010.

Note: For fab40 templates to work in SharePoint 2013, we need to install fab40 WSPs in both 14 and 15 hive compatibility.
We need to install WSPs one by one.
It will take longer time to install the WSPs in 15 hive compatibility

Add-SPSolution “c:\Solutionname.wsp”

Deploy the solution

Install-SPSolution -Identity Solutionname.wsp -GACDeployment -force -CompatibilityLevel {14,15}
If the above command throws any error then you we need to install solutions first in 14 compatility and later in 15 hive.
14 Hive:
Install-SPSolution -Identity Solutionname.wsp –GACDeployment -force
15 Hive:
Install-SPSolution -Identity Solutionname.wsp -GACDeployment -force -CompatibilityLevel 15
We are may also come across with the below error while we do a visual upgrade.

The following sites are using templates that are not yet supported after upgrade:

http://servername/samples/ – #0
http://servername/samples/ – #1
http://servername/samples/ – #2
http://servername/samples/ – #3

• Create one file .xml and copy the below code.
• Copy the file to the below location to \TEMPLATE\1033\XML\
• Follow the remaining steps from the above link to complete the migration.