  In arXiv:1907.07688 Balthazar, Rodriguez and Yin (BRY) computed the one
instanton contribution to the two point scattering amplitude in two dimensional
string theory to first subleading order in the string coupling. Their analysis
left undetermined two constants due to divergences in the integration over
world-sheet variables, but they were fixed by numerically comparing the result
with that of the dual matrix model. If we consider n-point scattering
amplitudes to the same order, there are actually four undetermined constants in
the world-sheet approach. We show that using string field theory we can get
finite unambiguous values of all of these constants, and we explicitly compute
three of these four constants. Two of the three constants determined this way
agree with the numerical result of BRY within the accuracy of numerical
analysis, but the third constant seems to differ by 1/2. We also discuss a
shortcut to determining the fourth constant if we assume the equality of the
quantum corrected D-instanton action and the action of the matrix model
instanton. This also agrees with the numerical result of BRY.
