Thank you. I’ve bricked the outside up now and even pointed the back of the course up so it’s extra neat and watertight. Here’s a photo just before it went dark. I’ll get the rest of the wall cleaned up and treated and hopefully it’ll dry out soon
I wouldn't go any further than what you can see, no point adding to what is already a pretty large repair.
If there is more mortar or brickwork that's loose, then I'd recommend a professional looksee just so to be sure.

