For discrete elliptic curves, can you find G, if you are given b and B? I know you cannot find $b$ if you are given $B$ and $G$, where $B = [b]G$, 

but can you find $G$ given $b$ and $B$?
$G = [b^{-1} \bmod q]B$ where $q$ is the order of the group generated by $G$, assuming $\gcd(b, q) = 1$.