Is the supplicant sinful if he marries a girl other than the one with whom he had an illicit relationship, and who threatens to curse him if he does so?

A Muslim man is not permitted to converse with a non-mahram woman except out of necessity, to the extent of that necessity, and within the bounds of propriety. Therefore, the prolonged period of your conversation with this woman is not permissible according to Islamic law.

Both of you must repent and seek forgiveness for this. If you wish to marry her, then propose to her through her guardian according to Islamic law. Otherwise, seek another woman of religion and good character.

It is not a prerequisite that your marriage takes place, and you will not be sinful if you marry someone else. She does not have the right to prevent you from marrying someone else.