Templar and Hospitaller Ties

I believe the Knights Templar and the Knights Hospitaller were the right hand and left hand of the same organization. Its more than both being Christian military orders. Both were founded in Jerusalem in 1119 AD. The original stated mission of the Knights Templar was to protect the pilgrims traveling to Jerusalem. Yet in those early years the Knights Templar devoted their time exploring and excavating around the Temple Mount. It was the Knights Hospitaller that protected the travelers. Coincidence? I think the two had an agreement which King Baldwin of Jerusalem was likely aware of. He was the one that granted the Knights Templar access to the Temple Mount and certainly would have been aware that the Knights Hospitaller were the ones protecting the Christian pilgrims. 

Years later when the Knights Templar fell out of favor and were persecuted until the order was dissolved it was the Knights Hospitaller that received their seized lands. On the surface that appears to be a perceived slight but it was actually keeping the assets in house. An early practice of moving the money from one shell business to another. Many of the Knights Templar that escaped execution joined the Knights Hospitaller. It was a lateral move as the two had similar structure and practices.