At Rep. 442b-443d, it sure looks as though Plato is arguing, even if imperfectly, that internal justice implies ordinary justice. In the passage below, which Sam Rickless drew attention to, it looks as though he wishes to argue that acts of ordinary justice lead to internal justice: and then the one trait would imply the other, because anyone who consistently carried out just deeds in the ordinary sense would thereby have established in his soul the 'healthy' state of internal justice.
The argument looks weak and abbreviated, to be sure, yet it does seem to be an argument. Moreover, it's an argument which, apparently, is part of Plato's aim to confirm that his definition of justice is correct. (Plato confirms the definition at the end of IV, before going on to argue later, in VIII and IX, that justice so defined makes for happiness and other good things.)
So isn't Sachs simply mistaken in alleging a fallacy? Better perhaps to observe that Plato's arguments are weak and then to ask the (surely fruitful) question of why Plato supposed that what he said was sufficient--what view of just and unjust action led him to suppose this.
“Healthful things surely engender health and diseaseful disease.” “Yes.” “Then does not doing just acts engender justice [444d] and unjust injustice?” “Of necessity.” “But to produce health is to establish the elements in a body in the natural relation of dominating and being dominated by one another, while to cause disease is to bring it about that one rules or is ruled by the other contrary to nature.” “Yes, that is so.” “And is it not likewise the production of justice in the soul to establish its principles in the natural relation of controlling and being controlled by one another, while injustice is to cause the one to rule or be ruled by the other contrary to nature?” “Exactly so,” he said. “Virtue, then, as it seems, would be a kind of health [444e] and beauty and good condition of the soul, and vice would be disease, ugliness, and weakness.” “It is so.” “Then is it not also true that beautiful and honorable pursuits tend to the winning of virtue and the ugly to vice?” “Of necessity.”
ta\ me/n pou u(gieina\ u(gi/eian e)mpoiei=*, ta\ de\ nosw/dh no/son.
ou)kou=n kai\ to\ me\n di/kaia pra/ttein dikaiosu/nhn e)mpoiei=, to\ d' a)/dika a)diki/an;
e)/sti de\ to\ me\n u(gi/eian poiei=n* ta\ e)n tw=| sw/mati kata\ fu/sin kaqista/nai kratei=n te kai\ kratei=sqai u(p' a)llh/lwn, to\ de\ no/son* para\ fu/sin a)/rxein te kai\ a)/rxesqai a)/llo u(p' a)/llou*.
ou)kou=n au)=, e)/fhn, to\ dikaiosu/nhn e)mpoiei=n ta\ e)n th=| yuxh=| kata\ fu/sin kaqista/nai kratei=n te kai\ kratei=sqai u(p' a)llh/lwn, to\ de\ a)diki/an para\ fu/sin a)/rxein te kai\ a)/rxesqai a)/llo u(p' a)/llou;
a)reth\ me\n a)/ra, w(j e)/oiken, u(gi/eia/ te/ tij a)\n ei)/h kai\ ka/lloj kai\ eu)eci/a yuxh=j, kaki/a de\ no/soj te kai\ ai)=sxoj kai\ a)sqe/neia.
a)=r' ou)=n ou) kai\ ta\ me\n kala\ e)pithdeu/mata ei)j a)reth=j kth=sin fe/rei, ta\ d' ai)sxra\ ei)j kaki/aj;