The use of a dead woman's credit card and a criminal record is definitely not enough to prove that a person is guilty of murdering her. There has to be some other evidence, such as witnesses placing the defendant and the decedent together before the time of her death, or even video evidence.
You can't spend money that doesn't exist. And in the case of the deceased, that is exactly what happened. If it isn't a crime, it should be. Even if it were the person's first offense this is a very large amount of stealing that someone has to pay for and they should be punished equally.
To prove guilt, there must be no doubt that a person has committed a crime. Since it is possible that a woman may have lent her credit card to someone with a criminal record before meeting her demise, then doubt exists. It is not likely but it is possible and therefore, one must be presumed innocent.
Alone, use of a dead woman's credit card and a criminal record are not enough to prove guilt. With the criminal standard being "beyond a reasonable doubt," there must be more than mere use of a card or past criminal conduct to convict. While it is reasonable to consider those factors, it is not enough by itself.