The mail has been rather heavy this week. A lady in Manhattan writes: Dear Mr. B.,

I just received my bank statement from Manufacturers Hanover Trust Co. and have been credited with $3 billion to my account. My husband said it couldn't be the bank's fault because they don't make errors. He said I must have messed up my checkbook again. I went over every stub and could not find a $3 billion mistake. I found one for $17.50 and another for $60, but none for the larger amount.

I am certain someone put the $3 billion in my account by mistake. My question is, should I notify the bank or keep the information to myself in hopes that Manufacturers Trust doesn't discover it?

Please advise. -- Mrs. Paul Conway Dear Mrs. Conway,

Your husband is correct in saying that large banks do not make mistakes. Therefore, it seems to me that you may have deposited $3 billion in your checking account and forgot to keep the receipt. Or perhaps someone with the same name deposited $3 billion in her account and you were credited with it.

I'd advise you not to tell the bank as they will get very upset with you for bothering them on such a minor matter. They will either ask you to move your account to another bank or will bill you with a service charge for making them go into their computers.

I would leave the $3 billion in your account for six months. If you don't hear from Manufacturers Hanover by then you can start writing large checks on the assumption that, even if the bank made such an unlikely error, they will be too embarrassed to admit it. Sincerely, A.B. Dear Sir,

I live in Key West and do a lot of Scuba diving off the coast of Florida. For the past three months I keep hearing a lot of shoveling and digging when I'm under water. Is it possible that the Russian Combat Brigade is digging a tunnel from Cuba to Miami? If so, should I notify President Carter? -- Lee Fentress Dear Lee,

Please don't say anything. President Carter is having enough trouble getting his SALT Treaty through. If Sen. Frank Church hears about the tunnel he'll demand that the President do something about it.

The Soviets will maintain that they are only building the tunnel as a training exercise. Carter will have to take their word for it because he still doesn't know what the Soviet brigade is doing in Cuba. Besides you're not sure the tunnel is being dug by the Russians. It could be our own CIA digging one to Havana to find out what is going on there. -Sincerely, A.B. d Dear Mr. B.,

I'm a marshmallow salesman and I met this nice guy in a bar in Bloomington, Minn. He said he was the manager of the New York Yankees and he bought me a drink. Then he hit me in the mouth. I had to have 18 stiches on my lip. Now he wants me to do a Lite beer TV commercial with him. What do you think? Yours truly, Bloody Manny Dear Manny,

As soon as your lip heals I'd do it. There is a lot more money to be made in selling beer than in toasting marshmallaows. But tell him if he socks you in the mouth again, you will hit him over the head with a beer bottle. -- A.B.