Can you date thus wall by its brickwork?

[brambal]

The first photo shows the white-rendered gable end of my friend's semi-detached house, which had a loft conversion in 2013 before she bought it - you can see the newly constructed rear dormer behind.

The second photo shows that the other (right) side of the semi doesn't have a gable end, so she's trying to work out if her gable end is original (1937), or whether it was constructed at the same time as the loft conversion.

There are no conversion plans online because the conversion was done under permitted development (no permitted development certificate was applied for, but when a neighbour requested enforcement action, it was closed with no action).

The third photo shows the only bit of the gable that has exposed brickwork. It looks modern to me, rather than original, do you agree?

(She wants to know, because if its modern its also likely to have cavity wall insulation like the dormer, but if its original then it will be solid brick like the rest of the house and have no insulation).

Are there any similar pairs nearby?
The gable front has thrown me off a bit, as the pair is not symmetrical.

It would be very unusual to have 1930s semis that weren't originally built as a matching pair.
The gable end is new.

Thats a single brick thick/cavity wall construction pattern. Old solid walls are typically 2 bricks 'thick' and have a different patterns depending on age/what was in fashion at the time (I forget the name of them all but you will be able to lookup online)

Easiest way to investigate insulation will be to drill a small hole in the mortar and poke a stick in to see. If its spongy it has insulation in the cavity.

Off topic, but I'm concerned that those extra wide grey bricks have cracked vertically in a straight line. Why?

I think typically, those houses had 'hipped' gables.

The white gable is new. It could be rendered block work or timber frame.
The neighbour has a hip roof. No one would change from a hip to a gable unless they had a loft conversion. So the hip is original.
The grey bricks are a bit odd, as bricks are usually 65mm x 215mm. These are 50x225 and look like they are for interior application as there is no face (from what I can tell).
It’s a near certainty the wall is insulated, but as a PP said, drill a hole.
The fractures are probably fine, but worth checking every year or so.

Thanks all. For context, the exposed brickwork is inside the eaves cupboard, so just the lower right corner of the gable triangle.