Anonymous to the receiver-- is it possible?

Does Zcash support anonymity to the reciever? For example, A sends some coins to B. But B does not know who sent him the coins, except that A tells B about the money, together
with the verification methods.

The recipient cannot see the sender’s address if it’s coming from a shielded address.

Any identifying information such as a reply address would need to be included in the memo field

Thanks to the colleagues above. In my research, only the source address should be shielded. The amount of each transaction, and the balance of each account should be
visible to the public. Does the technology employed in Zcash support such demands?

I suggest you should read more about Zcash viewing key.

I am not sure what exactly do you need but viewing key can reveal all incoming transactions (including the amount, block height, and memo) into a recipient address.

That is a major privacy leak, if anyone can see balances then funds can be tracked.

A fully shielded z2z tx hides all info except that the tx occurred and how much of a tx fee was paid as you can see here.
https://explorer.zecmate.com/tx/d8e1368c36594fe97c2c50d0ba670f75b4993b54f8e61fe3300af6adf3c09347
This applies to the reciever as well and a name or something would need included in the tx to be able to identify the sender, otherwise they’re anonymous.

A shielding or deshielding tx (t2z or z2t) reveals the amount and the transparent partys t-addy (either sender or reciever) and the tx fee, the shielded z-addy remains hidden in either case.
https://explorer.zecmate.com/tx/60b149cba443dd99633542ba9151d9d730709f1afb8524a4e93581b3304c9625
And t2t is just like a bitcoin tx

Thanks to the colleagues above.
In fact I am not treating the Zcash (and the technology behind) for currency usage. In my research scenario, users can anonymously donate to unlucky persons. The public can see in real time how much money has been raised. I think this can be ascribed to the application of blockchain in charity.
I am reading the documents of zerocoin and zerocash, before I can read the document
of Zcash. But it takes time for me to comprehend.

You can definitely use viewing key for this.

@oxear A good resource here is https://zips.z.cash/zip-0310 which describes what information can be revealed with Sapling viewing keys, and what guarantees the observer has about that information. In particular, a Sapling full viewing key will reveal information about what notes are received and their memos, but will not reveal the sender (unless the sender identifies themselves in the memo). It will also reveal the details of all outgoing transactions, which might be useful in a charity context (to see where the donated funds are going), but can be separated from just the ability to see incoming transactions if necessary.