This is the tag on the side of the transmission you are looking at, correct?
Hopefully someone will come along with better info for you. In the meantime, this may help. I don't know of an open publication of the industrial serial numbers, like we have for Ag tractors. The 166696 number puts it in the 1973 build year of 350 and 450 crawler s/n lists I access. From looking for other industrial tractor build years in the past they seem to fall in with the crawlers, so I would say 1973. You can look at auction sites to compare the serial numbers to the years they show for an idea as well.
I don't see a J used looking at the serial number info in 300 introduction document in the JD Parts Catalog PC972, and the type of format is different on the serial number tag. The 300 used a type series like: 4W1C, then the 6-digit number. The 300-J look like he may have a later 300 related to the 301 (which used that type of format), as it appears there was overlap in build years. The 301 used a J to designate Diesel, Collar shift Transmission with reverser and a Loader.
He may want TM1087 for the 300B. You can call the JD Construction and Forestry Bookstore and ask them (have the tractor info in hand when you do). Here is a link to the site, scroll down the page and you will see the help box on the left side. click on that and there is a phone number and other contact info.
JD Construction and Forestry Bookstore