Yes the same bag. I think it's called a Willis Murphy crossbody. Here are the before photos:
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All the photos above are daytime photos. It's a dark taupe color
This is after one bath and one treatment of conditioner. Photos taken at night. Left is no flash. Right is with flash.
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It is a Murphy bag. I think that might be mold on the corner in the first set of pictures. It is hard to tell, but that would be my guess from the pictures..
You can go over the bag with a solution mixed 50/50 of denatured alcohol and water to kill the mold spores. (If you don't have denatured alcohol, rubbing alcohol and water would also work. Vinegar and water would also work.) Since it may have mold, it may be a good idea to put it back out in the sun periodically since you've conditioned, but just watch the leather to make sure it doesn't get too dried out. If it does, condition. A conditioner that also says it inhibits mold would be good for it.
Based on your after-conditioning picture, I would say keep conditioning at least every 24 hours or so. It is way too soon to figure what else you might need to do the bag at this point. Bags will often change dramatically as you keep conditioning them. I think it will be beautiful.