Outlook Integration of Tasks
The default emails that are sent for an approval workflow are broken. The idea is that users can click on the "Open this Task" button directly within Outlook. But this button is broken (since 2010?)
Beside that there is no such button when using Outlook Web Access.
Therefore there is no way direktly hup into the according task to edit this approval workflow.
This issue should be fixed and the email itself should contain a link to approve or reject this wf directly.
You need to think outside of your environment. For example, if using a hyperlink what would your users do if the URL is an internal URL and they are external to your farm. eg on their phone?
The simple answer is an email reply to. So when you reply "approved" to the approval email it goes to a document library and the email can be actioned automatically via a default workflow on said library.
Note: workflow on the document library needs to be created by a SP dev.