I have a wallet on Bitcoin Core with addresses that are receiving and will receive payments in the future (which I can't change); for this reason I cannot send my bitcoins to a new wallet; that said, how can I export my wallet from Bitcoin Core to another client (SPV: I'm unable to download 30GB and more)? Thank you very much
It's advisable to send bitcoins from one wallet to another. Messing with private keys always increases the risk of theft or user error.
If the reason that you want to change to an SPV wallet is that your harddisk is getting full, then update to the latest Bitcoin Core version (0.11) and have a look at the prune option. Sorry, the prune option actually disables the wallet, so that's not useful in your situation. Hopefully that will be fixed in the next version.
Note that an SPV wallet requires significantly more trust (in other people not lying to you) than Bitcoin Core.
As a more direct answer, you can export private keys from Bitcoin Core and load them into most(?) SPV wallets. I believe this should give you the details: How do I export my private keys from my Bitcoin-Qt client?