We observed the 19 keV neutron decay from the 3.388-MeV state of $^{12}\mathrm{B}$ by measuring $^{11}\mathrm{B}$-neutron coincidences in colinear geometry at several angles. The ratio of this yield to the yield of particle-stable $^{12}\mathrm{B}$ nuclei is a measure of the excitation energy of $^{12}\mathrm{B}$ fragments produced in the reaction. The extreme kinematic focusing of the 19-keV decay enabled us to obtain the dependence of this ratio on fragment kinetic energy. For $^{12}\mathrm{B}$ nuclei emitted with kinetic energies $\frac{E}{A}$\lesssim${}15$ MeV the ratio is surprisingly constant; for $^{12}\mathrm{B}$ nuclei of higher kinetic energy it decreases monotonically.