Wow I just wrote up a nice big post for you and my internet crashed and I lost it.
In a nutshell: You need a test kit to even know if you're cycled or not, and to monitor your water changing. Eels are very sensitive, you have to have good water conditions for them. With a 1.5' eel in a 15g tank, i'm sure the bioload is huge.
I've never personally kept a moray, but here's some things i've read about them.
1. The “secret” of keeping morays are to understand that these animals are very easily stressed if not given the right environment. And if they feel stressed they’ll stop eating and slowly fades away over 2-3 months, which explains many of the rumours surrounding these fishes.
2. First of all I would like to stress that these fishes are not really freshwater fishes, even if they can be found from time to time in freshwater. They are much rather kept in brackish waters. This said I should add that it is possible to keep these fishes in freshwater more permanently, however the fishes are much more sensitive in freshwater and therefore this is not recommended if you don’t have extensive experiences with these species and even then brackish water is preferred.
3. recommend a big aquarium, at least 540 L/120 Gallon for these fishes which grows to about 60 cm. The aquarium should be decorated with a lot of hiding places.
4. fishes if well taken care of live to be 35 years old they might become a long time acquaintance
So... the fact that you don't have a test kit scares me. Also the small tank is going to add a ton of stress.
He will require a very big tank, so you'll have to invest in tank, lighting, new filtration, new substrate, new decorations, new heater, etc.
I know that you said you have a tank picked out for him, but what size is it?