It is clear that you are an extremely sensitive person who wants to do the right thing. In Judaism we are taught that there are two dimensions that need to be rectified.
The first is to be sorry and to do whatever possible to ensure that such an occurrence does not repeat itself. This is accomplished by sincere regret and by deciding to live in a way in which the wrong behavior will not reoccur. Remorse for the past wrong and determination not to repeat it are essential elements to achieve correction.
However, there is another facet that needs to be rectified in your case. If any financial damage was done to the other party it needs to be restored. The most ideal and complete form of repentance would be to return the money to the person.
If the person cannot be located, the Rabbis teach us that we should take the amount of money in question and donate it to some kind of a public project such as a park, or even street lighting. That way there is a chance that the ‘victim’ will also benefit from the public works and, in a sense, get their money back. This concept is applicable in your case as well. Even if the person is deceased he will receive the compensation in some form in the Afterlife and therefore I likewise suggest that you donate the stolen money to a worthy public cause. May you have much happiness and success.