Hi,

After activating the developer mode, under the settings you can see a menu named groups, there you can create your new user group. 

As it is created from the front end, currently it will not have an external id, so switch the view to tree view and export the created new user group. Now you will get an external ID to the group.

For generating the external ID, you can have a look at this video: Generating External ID in Odoo

You can see the external id of a record from click the lady debugger button near logged in users name in the form view and click the View metadata from the list, in the opening pop up you can see XML ID, copy it.

Now open the purchase order form view where the approve button exist, click the debugger button and click the edit form view option, in the opening pop up inside the architecture tab or in the records in the inherited views tab, there will be code of the button, currently for the button the inside the groups tag there will be the external ID of the managers group, you can change it with the external id of newly created group. 

Then this  button will be visible for this group of users.

The same can be done via code/ custom module too.

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Thanks