What is the ruling regarding my demanding a financial sum owed to me by my former partner, given the existence of witnesses to the verbal agreement, namely a mutual friend and my wife, who is the partner's sister?

If you sold your share in the project to your partner and relinquished it for an agreed-upon sum, then you have the right to demand it. If he refuses to pay while he is able, then he is a procrastinator and an oppressor, and it is permissible to refer him to the Shariah authorities. However, if he is in straitened circumstances, he must be given time until he becomes solvent. The testimony of a wife for her husband is not accepted by the majority of scholars. As for the testimony of a friend, it is accepted, even if he is amiable, according to most scholars.