Praise be to Allaah.
A woman cannot be a mahram for anyone else. The mahram is a man who is forbidden for marriage to the woman because of blood ties, such as her father or brother; or a mahram through marriage, such as her husband, husband’s father or husband’s son; or a father or son through ridaa’ (breastfeeding, i.e., the father or son of the woman who breastfed her), and so on.
It is not permissible for a man to be alone with a non-mahram woman or to travel with her, because the Prophet (peace and blessings of Allaah be upon him) said: “No woman should travel except with a mahram” (saheeh, agreed upon). And he (peace and blessings of Allaah be upon him) said: “No man is alone with a woman, but the third one present with them is the Shaytaan” (narrated by Imaam Ahmad and others, from the hadeeth of ‘Umar (may Allaah be pleased with him) with a saheeh isnaad).
And Allaah is the Source of strength.