When sending to private address there will be trace of public address as sender, but no address where transaction went. You do not enter private key to search your transactions, as you can use txid. Also you can see transaction inside your wallet.
☆T (Public) ⇦ OUT Yes ▷ AMOUNT 21.1.2018 18:06:10 ▶ (Z Address not listed by wallet!)
★Z (Private) ⇨ IN Yes ▷ AMOUNT 21.1.2018 18:06:10 your Z address here
Here you can see example of transfer from public to private address. There is no trace of receiving address.
http://explorer.zclmine.pro/tx/b361c542a6a32729a8bd4fc71c761947939105bf1be38e640ffcd51bc3c346d3