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My question is:
Will B node receive from A all the context from the origin even if the two nodes are not the same storage type?
As a full node contains all the data necessary to participate to the network as a bootstrap peer (namely all the blocks of the chain), it is indeed possible to bootstrap a node (archive, full or rolling) from a full node.
Only the rolling nodes cannot participate to the whole bootstrap effort as they don't recall the complete chain, but only a small rolling window.
N and its corresponding operations are "applied" on top of the context N-1 to compute context at level N.
I might have found the answer from this blog post from Nomadic Labs:
An important thing to note is that running a full node is enough to maintain the full chain history. Indeed, archive nodes do not need to use archive peers to bootstrap their archive, but only full peers, as the chain data is enough to apply the chain and construct the context archives. In other words, the network does not lose any security by switching to full as the default.