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This idea is very close to my proposed conception. Actually this idea can be completed with NFC technology cos the speed of pairing and connection of NFC is extremely high.
The main idea is to separate some amount of bitcoins, store and transfer keys.

I didn't understood a few things. How recipient can be sure that the payer didn't make (or someone else) the duplicate of the key?

The recipient of the funds receives two keypairs: the one that the payer's smartphone has generated and the one the payer's smartcard has generated. The one from the smartphone is in the clear, he can take a look at it. The one from the smartcard is encrypted and can only be decrypted by the recipient's OtherCoin card. The payee imports the secure (encrypted) half into his OtherCoin (the OtherCoin verifies that the encrypted key came from a similar OtherCoin card). If the OtherCoin card has accepted the encrypted half, the user can be sure that the sum between the key that he holds and the key that the card holds is a private key for the funds and that it hasn't been used before.

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And can the recipient get that key without been proceed this transaction online?

The recipient gets the key in an offline transaction. The only thing he can't verify offline is the balance (how much that key is worth). He knows for sure that he holds the key to a particular Bitcoin address (he just doesn't know what that key is, half of it is stored in the OtherCoin card). Part of the OtherCoin service will be "certifying" balances for people that want to transact completely offline. Most users however will just look at the blockchain to see how much a Bitcoin address is worth.

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And can the recipient transfer key which he got from the payer to another recipient ? without been proceed and verified this keys online first

Yes, they obviously can transfer it away, to a similar OtherCoin card. The guarantee comes from the fact that each and every OtherCoin card in the chain verifies that the sender is also an OtherCoin card, meaning that it has followed all the rules of the system (has not made copies of the key, etc). Think of it as a tamperproof computer sitting inside your smartphone - it guarantees that all participants in the protocol follow certain rules and even though it runs inside your smartphone you can't control what it does.

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can it be multiply offline transactions?

No, a key is either transferred via OtherCoin to a similar card or revealed to the user to be used in a Bitcoin transaction. It's either one or the other, as soon as the card gives you the secure part of the private key, it destroys it from its storage, so it can no longer be transferred via OtherCoin. It also destroys it as soon as it's transferred to someone else via OtherCoin.

So, to summarize, the security comes from the fact that all participants use the same hardware and software and that they cannot change the way the software works. They can't change the software to tell it to _not_ delete a private key after sending it or tell it to reveal its keys. It's a black box as far as the smartphone is concerned, you send some input to it and gives you some output, you don't control how it processes your input. What it does though is fairly public, it's described in the whitepaper and I can describe it further if needed.