How can one deal with the desire to marry a girl met online, given concerns about her continued communication with others after marriage, especially since there are positive signs in her?

It is advised to fear Allah and avoid speaking with marriageable women (non-mahram women) because it is a gateway to evil and corruption, and a step from the steps of Satan. A woman who converses with men and gives them her pictures is not pleasing in her religiosity, and should not be sought for marriage until she becomes righteous. The questioner is advised to marry someone who is pleasing in character and religiosity.