Can motor blow out if put a almost new transmission about 40k miles the motor has 137k miles?

40k isn't almost new.. no it shouldn't hurt the motor but the motor is getting up there and very well could blow regardless of the transmission. You may also run into issues with the transmission if it wasn't rebuilt but pulled from scrap if it's sat for a long period it may fail soon too.

The motor life has nothing to do with the transmission. Not changing the oil and filter every 3,000 miles will shorten the motor life.

Almost new? 40k??!!

.5k would be "almost new" in my opinion.

But my answer is: NO.

A new(er) transmission will not injure an engine. The mileage of an engine and transmission do not need to be "matched".

Mileage doesn't effect that, it's how the transmission is built, what type of car and transmission do you have/plan to get?

Yes it can. Engine drives the torque converter on the trans. Thats it. Everything else is based on ur engines rpms and other electronic readings.