  Recently quantum-like representation algorithm (QLRA) was introduced by A.
Khrennikov [20]--[28] to solve the so-called "inverse Born's rule problem": to
construct a representation of probabilistic data by a complex or more general
(in particular, hyperbolic) probability amplitude which matches Born's rule or
its generalizations. The outcome from QLRA is coupled to the formula of total
probability with an additional term corresponding to trigonometric, hyperbolic
or hyper-trigonometric interference. The consistency of QLRA for probabilistic
data corresponding to trigonometric interference was recently proved [29]. We
now complete the proof of the consistency of QLRA to cover hyperbolic
interference as well. We will also discuss hyper trigonometric interference.
The problem of consistency of QLRA arises, because formally the output of QLRA
depends on the order of conditioning. For two observables (e.g., physical or
biological) a and b, b|a- and a|b- conditional probabilities produce two
representations, say in Hilbert spaces H^{b| a} and H^{a|b} (in this paper over
the hyperbolic algebra). We prove that under "natural assumptions" these two
representations are unitary equivalent (in the sense of hyperbolic Hilbert
space).
