The plant in the photo is suffering from a severe lack of light. It is dying. Although these are shade lovers in the tropics, in NY they can take some direct sunlight outside in the summer. That said, do not take this plant out, it will burn. It should be placed near a very bright window for a couple weeks, then put right in front of a window. Summer in the garden in the shade of a tree suits it fine. The flowers are highly fragrant and quite large.
The thin parts will never recover, so pruning might be in order. This looks like the species, as mentioned above, and not one of the many hybrids. It makes dimorphic growth, that is, 2 different looking stems. The flat ones make the flowers, the long pencil ones make the flat ones. The round stems also make the roots, although you can also get roots from where the slight notches are on the flat stems. This is a good time for pruning the plants because the longer days allow roots to form. Round stems with roots coming out can be buried shallowly in moist (never soggy) high organic matter soil. Pure peat is not the best. If that is what you have, mix it with maple leaves or some other non-walnut, non-oak leaves. (Walnut leaves inhibit roots, oaks leaves are high in tannin.) Epiphyllums don't like cold or dry, but if light isn't available, cool and dry will inhibit growth and you don't end up with a scary plant like pictured. Kept less than bone dry in a 50-60F room is better than in the dark corner of a warm room.
Good luck with your plant. In good conditions they grow fast and bloom frequently. Expect about 3 flushes of blooms from plants at least 2 years old. (In other words, don't expect bloom from the plants you get from the pruning.) The cycle here seems to be a flush of blooms in June, early August and then Oct. The Oct blooms are slow to develop because of the poor light and lower temps.
to all who responded. I have forwarded your advice to my friend who sends her heartfelt thanks as well! 
