4 to 5 months means nothing.
It depends how many hours and how easily he picks things up.
I would say Moonlight, even the first movement is a little steep for someone using an Alfred series.
HOWEVER(Some guy on the radio keeps saying that)
He should be passed the Alfred series by now. Method books are great to get your feet wet. I started that way and put them aside after about 3 to 4 months.
Your friend should do the same.
A Bach minuet is perfect
a scarletti sonata is another idea.
Bach's first Prelude is another idea.
Some Burgmuller ( La pastoral (Pastoral) in G major - L' Arabesque (Arabesque) in A minor
and much more.
Wow, Janice, just noticed. Been awhile. Hope things are well.
My belief, method books should be put away after the first six months, unless you have a very slow student.