My brain operates differently than a lot of other people. I don't try to find a way to profit from people for what should be an act of kindness. But that's just me.
That said, let's look at a couple of things.
Do the envelopes that the dividend checks come in say something to the effect of ""address correction requested"? All you have to do is write on the envelope something like "Deceased. No longer at this address." (I'm not sure if you can expect to be paid for this.
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The company that issues the dividend checks will realize at some point that the checks are not being cashed (please tell me you aren't cashing them!). They will try to contact the rightful owner and, if they are not successful, will turn the account over to the State. The State will place the stock and dividends in an account for unclaimed property and attempt to locate the owner. (Other unclaimed property the State may be holding includes property from safe deposit boxes, money in closed bank accounts, unclaimed refund checks, etc.)
Now, let's look at some of the legal aspects of this matter. (I am not a lawyer and am not giving legal advice.) I called my local Postal Inspector and posed this scenario to her. She said that there are at least 2 legal concerns here both revolving around "improper use of mail".
By not returning the dividend checks to the issuer you are
improperly using the mail.
If you use the mail to obtain (extort) a reward from the heirs you are
improperly using the mail.
Keep in mind that these are
FEDERAL crimes!
I would advise you to either return the checks to the issuer or locate the heirs and forward the checks to them. You could send the heirs a short note telling them what you have done to help them (tracking down an address) and, who knows, they might send you a nice gift (or reward depending on how your brain is wired).
Be careful and good luck.