eventually you should raise the salinity higher than 1.005. At least 1.010 would be better as it is much more of a marine animal than freshwater.
Agreed. In order to set up a brackish tank for your Eel you will need a device for measuring salinity (hydrometer or refractometer), marine salt (sea salt or table salt will not create the right conditions, they lack the salts and minerals in marine salt) and some patience.
When you've got those vital pieces of equiment, only then can you really create a brackish tank. You will want to bring up the salinity slowly. Don't add the salt straight to the tank, and make sure your moray is feeding throughout, once they go off their food, they're difficult to get back on it.