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The crack is likely where a sand/cement mortar, (with zero movement accomodation)
has been used to fill the gap between the brick/blockwork and the wooden window frames,
and has delaminated from the former.
Is this property a 'keeper'?
If you only envisage being there a couple of years, your suggestion is valid.
If you see it as a long term home, maybe invest a little more in the materials.
The labour will not be too different.
Measure the crack.
Lets work with 2mm.
If your exterior filler has only a 10% movement accomodation, you will need a 20mm wide fillet of material.
The Soudal Fix All is probably closer to 40%, meaning a 5mm wide fillet.
OK - how about for this guy
https://lfgss.microcosm.app/api/v1/files/0fc6338fb1283b8e45b981eeb0705fb693ef0258.jpeg
multi-tool to give the crack a mouth
clean / dust removal
PVA
Exterior filler
Re-paint
?