To be clearer in my problem statement, I'll attach a pic:
Basically, the original webbing is too frail to hold in daily use. I tried using new webbing and camouflaging it with the original, but the original wears off rather quickly.
So, if anyone happens to have the original strap for sale (in good condition, meaning that it doesn't rip when you try to rip it with your hands like paper or soft cardboard), or knows a store that sells comparable material, I'd be very happy!
In both of my authentic bags, the original strap and ring holders are basically dry rotted (I bought them from different stores and the original manufacturers are also different, so that's not the reason).