We report on the first measurement of the β+ and orbital electron-capture decay rates of Pr140 nuclei with the simplest electron configurations: bare nuclei, hydrogenlike, and heliumlike ions. The measured electron-capture decay constant of hydrogenlike Pr58+140 ions is about 50% larger than that of heliumlike Pr57+140 ions. Moreover, Pr140 ions with one bound electron decay faster than neutral Pr0+140 atoms with 59 electrons. To explain this peculiar observation one has to take into account the conservation of the total angular momentum, since only particular spin orientations of the nucleus and of the captured electron can contribute to the allowed decay.