Is it permissible to send a personal photo of myself, in which I am observing the proper Islamic hijab, to a non-mahram person (a man) via the internet, knowing that I am inviting him to Islam?

It is not permissible to send your picture to a non-mahram man because it is not permissible for men to look at women, as stated in the Almighty's قول (verse): "Tell the believing men to reduce [some] of their vision and guard their private parts. That is purer for them. Indeed, Allah is Acquainted with what they do." Scholars have determined that it is not permissible for a woman to uncover her face if she knows that non-mahram men will look at her. You should also not be lenient in such matters, as it leads to evil deeds. You must clarify the religious ruling regarding what he requested from you to this man.