I've done extended fasting a few times and don't get headaches any more. Most people do when they do fasting for the first time, but usually only for the first few days. As someone else already said though, headaches will be the least of his problems.
Anyone who considers a fast that long usually has a reason for it - spiritual, weight loss, or autophagy (to heal a health issue). I'm on a few different fasting Facebook groups and I've seen a few people fast this long, but none who were a normal weight.
44 days is a significant amount of time. The body will start by burning the fat stores (in deep ketosis), but when the fat runs out it will turn to protein and start to metabolize muscle, including the heart and other organs. At 11 stone your husband might not have enough fat to safely fast that long.
Is he doing it under doctor supervision? Will he be taking electrolytes (sodium, potassium and magnesium are an absolute must).
I've never seen anyone who's only fasted half a day manage to go into such a long extended fast though. It's very, very hard mentally. I've done 21 days (when significantly overweight) and could have gone longer because I felt good. Mentally I'd had enough. I also refed very carefully.
Didn't David Blaine experience symptoms of starvation, breathing problems, heart palpitations etc. after fasting 44 days? And lost a huge amount of weight, which your husband can't really afford to do when he's already a healthy weight?
I'm very much pro fasting as it can have a lot of benefits. What your husband is suggesting though could be detrimental to his body and could potentially cause long term health problems.
My DH is also pro fasting and a similar weight and height to your DH. He only fasts a max of 72 hours per month, otherwise he would get underweight very quickly. A 72 hour fast can improve insulin sensitivity, reduce inflammation, increase metabolism, improve cognitive function etc. (there is research to support this), but I don't think your DH should be considering any longer than this.