Use of bitcoin client would be easier for him if all data expensive operations are done by third party client (for example my client) and his client would be able to verify found transactions and and them to his wallet.
that's what SPV clients, like electrum and multibit, does. they don't need you to download 70GB~ of data.
If the BTC electrum servers get taken down or offline or whatever then those who use it run the risk of losing their coins unless they have their private keys saved for their coins.
Anyone can run an Electrum severs[1] alongside their Bitcoin Core. The issue with doge electrum wallet was the lack of servers which is definitely not a problem with Bitcoin Electrum. People can set up their own nodes to connect to. You can also export the keys on Electrum if you need to; Wallet>Private Keys>Export.
[1]
https://github.com/spesmilo/electrum-serverJust because people can set up their own don't mean they will. I'll reference the Doge electrum again for this instance. Users could have set up their own and kept it going but that wasn't the case and those that were counting on that were mistaken.
It seems these servers are not quite stable or secure. I found Bitcoin-QT solid, stable and secure and easy to use. I believe if these features would be implemented in Bitcoin Core it would remain easy setup & run and secure. If there is any possibility losing funds because of not users fault, there is certainly more than one copy of private keys online and I would not recommend using it.
He can still use core. Find someone he can trust, and get a copy of the blockchain on a usb stick. Then he can use free WiFi to sync his wallet. A pruning node with no signature info ( when SegWit arrives) will save on disk space.
Transmitting more than 10GB of data is certainly not an option. I am trying to provide 100% complete support to reach a goal and redirecting users with half-done things to others isn't in my style, it simply does not works. If he had found someone he can trust about bitcoins then he would not ask me for support.
I will have a look at these wallets but currently looks client-to-website solution is best if full or pruned bitcoin node approach fails.