  In the present paper we extend the construction of the formal (affine)
Demazure algebra due to Hoffnung, Malag\'on-L\'opez, Savage and Zainoulline in
two directions. First, we introduce and study the notion of an extendable
weight lattice in the Kac-Moody setting and show that all the definitions and
properties of the formal (affine) Demazure operators and algebras hold for such
lattices. Second, we show that for the hyperbolic formal group law the formal
Demazure algebra is isomorphic (after extending the coefficients) to the Hecke
algebra.
