When is a transgressor considered righteously repentant, and is a period of one month sufficient to judge his righteousness?

Scholars have differed on the acceptance of the testimony of a transgressor (fasiq) after repentance. Some are of the opinion that it is accepted immediately upon repentance, arguing that repentance erases what came before it, and that forgiveness and legal rulings are obtained through it. Others, however, believe that repentance must be accompanied by rectification of deeds and the passage of a period of time during which thecerer's sincerity and uprightness become apparent. There has been disagreement regarding the precise duration of this period. Some have emphasized that the estimation of this period varies according to the penitent's situation and the manifestation of signs of sincerity in their repentance.