Consider the endothermic reaction, $X⟶Y$, with the activation energies $E_b$ and $E_f$ for backward and forward reactions, respectively. In general:

In the case of an endothermic reaction, the activation energy of the backward reaction will always be smaller than the activation energy of the forward reaction.

In your case, the backward reaction will look like this
$A+heat\to B$

Since heat is consumed during the reaction, the product will have a higher energy than the reactant. So $E_b<E_f$