Is a merger between two players possible in Monpoly?
Short version: With the exception of multiple players ending up winning, almost.

Longer version: There are a couple things where this is different from the official rules. Because trades are legal within the rules, there's nothing stopping Player B from trading all of his property and money to Player A, in exchange for a dollar or something like that, and then after he loses being an outside spectator who attempts to help Player A.

However, you cannot sell/trade properties that have any houses or hotels on them. This means that if you want to stay within the rules, Player B needs to first sell his houses to the bank (at half value), and Player A would have to buy them back after the trade. Aside from costing extra money to re-build the houses, there are 2 situations where following the rules could be different here:


If there are a shortage of houses remaining in the supply, and Player B has properties with hotels on them, then Player A would be unable to re-buy the hotel after he gets the property.
If there is a shortage of houses or hotels in the supply, and the third player could build the houses or hotels, then he can bid on them to attempt to win them in auction. Player A may either have to pay even more for them, or end up losing them to the third player.


The other thing that's outside the rules is that if Player A ends up winning, then by the official rules only Player A has won. But in your variant, Player B can claim to be as much the winner as Player A.