Hi-Lo Cryptogram

$\large{\begin{array}{ccc} && & H&H\\ + && & L&H\\ \hline & & & H & 1\\ \hline \end{array}}$

In the cryptogram above, the L position indicates a digit from the set $\{1, 2, 3, 4\}$ and the $H$ positions indicate a digit from the set $\{5, 6, 7, 8, 9\}$. All digits in the H positions are unique.

While there is not a unique way to fill in the cryptogram, the H in the sum's result can only be one particular value. What is it?