First off, there are many way's of cycling a tank. But the first thing I will say is to calm down. Look at your eel. If he's looking okay, relax. You've got the 45 set up, leave it freshwater at this time. Keep the filter on the established tank, and let the new tank settle in. After a day or two of this, transfer half of the media from your old filter, unrinshed, to the new tank, and transfer the eel. Do not feed for a couple of day's. Monitor the ammonia levels, or just do some small, daily water changes. Feed lightly during this period. After a few weeks to a month, there should be no measurable amount of ammonia, or nitrite. After this, the tank is considered to be cycled. Now you can very slowly adjust the salinity up, but not very fast. You want to change out about five gallons every other day or so, using full strength, or even better, brackish water. Keep the ammonia levels under check, changing the salinity could cause a mini cycle. If you see ammonia, stop changing the salinity until it goes away.