This is possible because all exchanges record these transaction but is same possible with Forex? Is there a universal way or central location where all the Forex transactions get saved?
Nope. The forex market is decentralized, and there is no single repository of all trades. There are about 10 market markers, aka the big players, that are considered the main players. These are big banks, XTX ++
The smaller players are usually using a combination of the feeds from these 10 or so to create their own rates.
The trades are not registrated back up the chain. So it is not possible to get a full transaction list of all fx transactions. Not for you, nor for anyone else either, regardless of resources