I'm trying to read the article *"Functional equations associated with addition theorems for elliptic functions and two-valued algebraic groups"* by Bukhshtaber,V. M. Russian Mathematical Surveys(1990),45(3):213 Russian text is available at MathNet.ru

This article gives a general solution of the functional equation $$f(u+v)=\frac{f(u)^2a(v)-f(v)^2a(u)}{f(u)b(v)-f(v)b(u)}.$$ It leads to [Bukhshtaber] formal group law of the form $$F(x,y)=\frac{x^2A(y)-y^2A(x)}{xB(y)-yB(x)}.$$

Unfortunately this article contains only a sketch of the proof. Additional typos do not help in decryption.

Are there any references to the full proof of this result?

Are there any simpler proofs of this result?