I once grew two forms of
Coryanthes speciosa... I now only grow
Coryanthes macrantha var. aurea and
Coryanthes vaquezii...
Anyways, right now, the
Coryanthes are sending out shoots, new roots, and possibly spikes... you want to still keep a little water on it, before it goes dormant in winter... I would watch those brown sheaths at the base of the bulbs so that water doesn't accumulate, but it's not a big concern. Those leaves look as if they are browning for winter dormancy... no big deal on them.
I would suggest planting your
Coryanthes speciosa in Spagnum moss in a basket, so the spikes, growths, and roots can escape out... but when you pot it up, make sure to carefully watch it for a week or so, as it is going from one extreme enviroment to another to yours... the ride would be very stressful... good luck on it, the plant overall looks good...
-Pat