Is there any change in the hybridization of $B$ and $N$ atoms as a result of the following reaction? $BF_3 + NH_3 \to F_3B \cdot NH_3$

(N/A) In $BF_3$,the hybridization of $B$ is $sp^2$,but in the adduct $F_3B \cdot NH_3$,the hybridization of $B$ changes to $sp^3$.
In $NH_3$,the hybridization of $N$ is $sp^3$,and it remains $sp^3$ in the adduct $F_3B \cdot NH_3$.
Therefore,the hybridization of the $B$ atom changes from $sp^2$ to $sp^3$,while the hybridization of the $N$ atom remains $sp^3$.