It is likely that Mehmet takes the black Stele at this time and did this to pay for his army with weapons, women and other spoils.
Mahmoud changes Heraclius's words towards his own idea that whatever his origin, Jesus Ieso had one Human will (Monothelitism).
Heraclius likely was unconscious of the difference and happy that he had more allies attacking the Sassanians for him.
=638 Heraclius capitulates (Ecthesis/SIN)=
Heraclius surrenders Syria and submits to Monothelitism with the Ecthesis, stating that despite alleged miraculous origins, Jesus Ieso had only one human will exhibited when he said "not my will but thy will be done" being clearly distinct from G-d's will. This view is compatible with Judaism and accurately reflects the standard position in Quraysh Islam.
The Ecthesis essentially commands the Ghassanids to submit to the Quraysh.