because I am not a structural engineer and if I said yes go ahead and it fell or sagged, you would not be happy with me.
I would tackle this problem in a completely different angle. I would find a door kit and all that fit inside the existing rough opening of the space where the original door was hung in.
Leave that header alone. to remove the header you have to remove the side kings and cripple studs. This will be difficult in getting new ones in because the new ones will not be able to fit in as tight as the existing ones when they come out because the wall there will settle a bit. You do not want to crack the walls so I would NOT do this.
Your existing door has a frame around it and space around that frame. With all that out you will have what is called the rough opening. That rough opening just might be big enough to accomodate your new door and frame kit. If not, you can shave some off the side jambs to get some extra small space, or if worse comes to worse, I would even consider shaving some off that top header to make space. That header is problably a 8 or 10 inch header. If you had to shave an inch off that for your frame to fit in that would work.
You need to open up that door and measure your rough opening and compare that to your actual door and frame kit and see where you are.
I don't even like suggesting that you can shave that header, but that call is up to you.