As mkwong98 said, to save changes to the ROM, you can go to the Debugger, then go to the File menu and use one of the Save commands: "Save ROM", "Save ROM As", or "Save edits as IPS".
However be aware that if you modify a RAM address, that won't be saved. Only changes you make to ROM addresses will be saved.
In the Memory Tools window, when you are viewing PPU memory or CPU memory, you can right click on any value to help tell if the address is a RAM address or a ROM address. In the right-click menu, if you see an item like "View in CHR ROM" or "View in PRG ROM", that tells you the address is a ROM address. If you see an item like "View in Nametable RAM" or something else like "View in ___ RAM", that means the address is a RAM address.
If you want to save a change to something you see in a RAM address, you will have to find a spot in the ROM that affects that RAM address. Here are some ideas how to do that:
A. Reload the game so everything is unmodified. In the Memory Tools, when you see a PPU RAM address value you want to change, you can highlight some of the bytes you want to change, right-click, choose Copy. Now change the View drop-down box to "PRG ROM", go to the Search menu and choose the Find command, then paste in the bytes. Maybe you can find the same byte values in the PRG ROM.
B. You can set a write breakpoint on the address (right-click, Edit Breakpoint, check the Write box only). Then open the Debugger window. When the breakpoint is triggered, the Debugger window will highlight some code that is writing to that address. Look a little bit earlier in the code to see if it is loading some ROM data you can change.
January 06, 2022, 09:49:49 am - (Auto Merged - Double Posts are not allowed before 7 days.)
Here is something else I just noticed:
In the Memory Tools, when the View drop-down box is set to "CPU Memory", "PPU Memory", "PRG ROM", or "CHR ROM", then the File menu Import command is disabled. But if the View drop-down box is set to any of the RAM types, then the Import command is enabled.
If you are looking at PPU memory that is RAM, you can right click on a value and choose "View in Nametable RAM", then you can Export and Import from there.
Be aware that Nametable RAM data will only make sense for the exact screen you are looking at. If you import at a different point in the game it might look different.
And since the game is often writing changes to the RAM, any import you do would only be a temporary change. But the export and import can help you experiment with changes and save a screen design you are working on.