When a new node connects to the network, other nodes start to share new transactions with this new node they got. But do they share their mempool, when a node disconnects from the network for some time for example? I think that the mempool size is too large and it would be difficult to share their mempool state, but maybe I'm wrong...
As far as I know mempool is like a waiting buffer or a waiting place for all the unconfirmed transaction before they are added to the
blockchain. While the Nodes is the computer that run the network software. Or in other terms it forms a network where
information can be shared or transacted.
Where the major function of Nodes are routing, storage, mining and wallet services. So if you know the difference beween Nodes and the mempool dude, You can able to find the right answer to your question anyway.