Change SSIS package authors
You would need to check the security setting of the package configuration (inside the package). The default for a package is "EncryptSenstiveWithUserKey", which means only that user can modify the package or read the connection manager objects.

You also don't provide how the packages are deployed. If they are deployed to the Package Store or SQL Server then the security setting mentioned above does not apply. If they are using file level deployment who executes the job or owns it can play a role in the issue you are having....meaning you will have to adjust the packages.