Bitcoin is transferred after initiation from the sender of the transaction through the internet.
The sender isn’t required to be connected to the internet to sign the transaction, but he is required to be connected to the internet to declare his transaction to the network so that they can record it. A transaction even signed, if not recorded within the blockchain is equivalent of it having never occurred.
In order for the transaction to complete, it has to be recorded on the blockchain and consensus should accept it.
The receiver does not have to remain connected to the internet as the transaction happens since the sender pays the transaction fee and gets the transaction recorded in the blockchain. Once the transaction is recorded, the wallet is free to sync with the blockchain and display the funds received. Even if the person isn’t connected to the internet, the blockchain explorer shall display that the funds have been transferred to the appropriate account. Whenever the receiver needs to spend the money within their wallet for a secondary transaction, they may sign the transaction offline, but whenever their transaction is broadcasted to the network, the miner verifies that there are funds allocated or present in the wallet to initiate the transaction.
To conclude, the receiver does not need an active internet connection to eventually receive the money, but however they do need an active internet connection if they wish their wallet to reflect the funds that they’ve received. They are required to have an active internet connection to broadcast their transaction after having received bitcoin to make a secondary transaction as well.