It's a easy question:

Imagine 2 nodes, they two have different transactions on them.

Node B finish to mine the block first, it broadcasts it and the network accept it.

Would this node inmediately continue proof of work even if the transaction pool is empty?

What would happen if he mine the block and new transactions would come in? He would to start again with the new transaction because the tx are included in the block so the hash of the block changes, so he each time new tx are added the node has to restart the PoW, Right?