Chimney modifications

[laferret]

Im installing a cooker under our old chimney and have reached an impass with the internal brick made flue sides. Left side can be removed without concern but with a mess. The right side forms the divider and goes up vertically to the old fireplace chimney. My problem is that I need to raise the bottom of the divider up above my lintel but don't want to risk the construction failing.
Can anyone shed some light on if it will be safe to do this because maybe further up its height it has been knitted in?
As you can see, the visible part sits almost completely on two angle cut bricks which are built in to the right side cheek.