Alternative solution maybe?

So, we know the last digits is 3 because the last digit of 39541 is 1, and the last digit of 41023 is 3, so 1*3=3. Then, we see that 1622090443 has two 0's so therefore 41023 is the only number that has 0's in it. Which means that 41,023 times 39541= something with zero's. So therefore, 41023 is the only possible number.

@neatlobster it is actually possible to get something with 0's with a number that has no zeros; for example, 51 * 2 = 102, but neither 51 nor 2 have 0s in them.
Cool observation though!