Help With a Speedmaster and its box

Hello all. I am new to this forum and have joined to seek advice. I am an attorney who is helping the widow of a close friend of mine handle his estate. She delivered a box to me last week with a shaving kit stuffed full of his watches, and about 8 empty boxes that I matched up to some of the watches in the shaving kit.
The nicest watch he had was a Speedmaster triple date that has a stainless case, a blue face and a black Omega leather strap embossed with an alligator pattern. He bought it new in 1999, and the warranty card was in the box. It is not running and she said it stopped many years ago and he never had it fixed.
My first issue is the box. The box is for a 30th Anniversary of the moon landing Speedmaster, it has the certificate of authenticity for one of those watches and the associated paperwork for that watch, however, the warranty card and original receipt that were in the box was clearly for the Speedy that I have. I have confirmed with her that he didn't have any other Omega watches and she said my friend kept the watch I have in that box.
I am trying to maximize the return for his widow. If there is a market for the special box for the moon landing watch, should I sell it separately from the watch? If so, how much are we looking at? The box and paperwork are in excellent condition.
Also, I need to decide if I'm going to have the Speedmaster serviced before trying to sell it. I am assuming that servicing the watch will cost $600 or more depending on its condition. The watch itself is in very good physical condition but the strap is worn and sweat stained on the back. I personally wouldn't wear it without replacing the strap. Any rough idea about what it's worth not running vs. running?

Here are some pics

I just looked at the receipt that is in the box. The date is for the 4th of December, but the warranty card says the 14th of December. The purchase price says $1800, with a discount of $540, for a total of $1260. I am assuming that the 30th Anniversary cost more than $1200 in 1999, right?

The certificate of authenticity for the 30th Anniversary watch has the serial number on it which matches the serial number on the outside of the box. My thought was exactly what you said about the shop switching the boxes.

The question for me is the date. The watch was purchased in 1999. That's the 30th anniversary of the Apollo 11 mission. If that box belongs to the anniversary watch, then we need to find the watch and maybe the warranty card if purchased new. Open the box and see if the card is in a compartment of the box or in one of the books. The anniversary watch is a 3560.50.00 and looks like this.

The blue dial watch is a 3523.80.00. I believe, a watch that was available in 1999, but the box I believe would be red not black, but the books , except that Apollo 11 book, may be the same for this watch and an anniversary watch. If the black box belongs to this watch then it could be a case of dealers putting a watch in any box as mentioned above.

The correct box for the 3523.80 is the standard red box that came in a white outer box. I’m sure the original box has deteriorated as the red box for my 3523.30 from 2000 has.

Let me know if you need pictures of both boxes.

I wish I

The outer box is perfect. No wear to speak of at all. I spoke with his wife again, and she said she only ever saw the Omega I have, and he kept it in this box. There is no other warranty card in any of the other literature. I am going to go to their house and search in his dressers and in his closet just to cover myself.

If I'm not mistaken, I think the latest price for servicing a chronograph is $900 in the USA anyway.

Omega currently charges $750 to service a chronograph.

OK, I think mine was more because it has a date and chronograph.

Anyone have a fair idea of what its worth as-is vs after a service and its running properly?

The instruction books are all for the moon watch. Nothing in them about how to work the features of the one I have.
I am going to do a thorough search of their apartment just to be sure.

Thank you for the advice. I was worried about that. The rest of the watches are dress style watches. There is a Rado, a Bulova, a Movado, a Longines and a TAG. All are quartz and seem to sell for $250 to $400 on eBay. Im going to have new batteries put in them and a mutual friend of ours does eBay sales as a business, and is going to be handling the quartz watches.
One last question. A mutual friend of ours approached me about buying the watch as-is but wants me to come up with a price. I know he can pay cash right away. My issue is I can't find one of these for sale on a strap, they are all on bracelet. Can anyone suggest a fair as-is price for this?