How to trigger the Submit for Approval field from a Custom Function/Webhook or Script?

How to trigger the Submit for Approval field from a Custom Function/Webhook or Script?

I have a Request Life Cycle where it's possible to press a status transition called "Submit for Approval" 

in the After section of that transition I want to trigger the Actions->Submit for Approval dialog window automatically.
How would I go about doing that in the easiest most correct way?

Also, when the technician uses the Actions->Submit for Approval  before changing the status, it doens't automatically move to the Status "Awaiting Approval"

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