Is it permissible to continue inviting university colleagues [to Islam] and to continue guiding and advising them, especially given their responsiveness and the absence of other female callers [to Islam]?

The call to Allah (Da'wah) is obligatory for both men and women, based on the general religious texts. The biography of the Prophet (peace be upon him) and his companions indicates the permissibility of men calling women to Islam, and women calling men, as occurred with our mother Aisha (may Allah be pleased with her).

However, in our current era, it has been observed that a man's immersion in calling women to Islam, or a woman's immersion in calling men, may lead to fitna (temptation/strife). Therefore, it is advised that this Da'wah be undertaken by a mahram (unmarriageable kin) of the one being called, or by the spouse, or by one of the mahrams. If this is not possible, then one should not engage in Da'wah to women unless there is certainty that fitna will not occur, and precautionary measures are taken, such as avoiding khalwah (private seclusion) with the woman, not prolonging the conversation, and being careful not to gaze at her.