The understanding of that part of MPP is somehow still blurred in my mind. I know that, for example Atomic Multipath Payments reason a bit differently and have one HTLC for every chunck of amount sent out there, but still I cannot grasp if the amounts can flow in the same channel or not.

My understanding of lightning is that the HTLC is stucked until the preimage of the hash doesn't arrive to the payer (source node). Thus, MPP with two HTLCs is only possible if the HTLCs are accomplished sequentially, not in parallel. But that would mean that the payment could suffer from being partially paid, because once the first HTLC is completed, every hop of the path knows the preimage for the hash, so if a second HTLC is triggered on the same path, the nodes can claim the funds without bringing the payment to the actual receiver.

This is what I can understand of MPP, I don't know if my understanding is correct or not. If it's correct, we shall wait for Atomic Multipath Payments for that "covergence" to happen.

Which means that, for my modelling problem at hand, a MPP payment is correctly modeled as a Min-cost network flow problem only if all the hops never converge to a single node (other than the destination)