I was told that full nodes don't store such a Merkle Tree; then where it is stored?
Nowhere, it is computed when it is needed.
I mean it must be stored somewhere to answer say SPV & alike trying to check their coins?
You don't need to store merkle tree if you have all data used to construct it. The whole blocks are stored, there are just block headers and transactions, nothing else is needed. If you have all transactions in a block, then you can hash each transaction and build merkle tree for that block, then you can check that merkle hash is correct. Full nodes don't need SPV features, because they have all data. Also, if some node is pruned, then still, it has N last blocks with all transactions, there is never a case where full node (pruned or not) has some "partial" block: for each block there are only headers or headers and all transactions.
Edit: Also note that SPV clients are indirectly connected with full nodes: there are for example Electrum servers and they require some level of trust, because they just tell you "this address has this balance, these transaction outputs are connected with this address", and so on. SPV clients just ask SPV servers for data, not full nodes. Only SPV servers talk to full nodes, and that servers need all data, so there is no case where full node need some part of a merkle tree to be stored permanently.