You cannot prove intention. Rabbis or anyone for that matter cannot read minds. Mind-reading is not part of Torah.
Rambam paskens that if beis din fails to tell the ger about mitzvot and their schar v’ onesh, the conversion is still valid (Issurei Biah 13:17) and the Magid Mishneh says that such a law for informing the convert about the mitzvot is simply not me’akev.