Why did tj marshall invent the fire extinguisher?

There is no indication that anyone named "T.J. Marshall" invented any fire extinguisher.

However, there was a US Patent 125,063 issued to Thomas J. Martin, on March 26, 1872, entitled "Fire Extinguisher".

Actually it was a type of fire standpipe and sprinkler in which water pressure from a reservoir and pump pushes water up pipes and into a building to a valve that can be opened to make the water spray out of nozzles.

This is nothing like what came to be known as the "portable fire extinguisher" we have now.