The Halacha is (as stated in the Kitzur Shulchan Aruch סימן יא - הלכות מזוזה) that when renting a house in the diaspora one is exempt from Mezuza for the first 30 days. For the first 30 days a rental is not considered a permanent residence.
כא: הַשּׂוֹכֵר בַּיִת בְּחוּצָה לָאָרֶץ, פָּטוּר מִמְּזוּזָה שְׁלֹשִׁים יוֹם, דְּלָא הֲוֵי דִירַת קֶבַע.
If a Ger (a convert) remains in the house they rented before the conversion, do they have to wait 30 days before affixing the Mezuza?
Do we apply the Ger is like a newborn rule, and it's as if they just moved in? Or do we look at reality and say that they've lived here for a long time and they have the status of permanency?
(In Israel one is obligated to affix the mezuza as soon as one moves in.)