The Mystery: I've mined some BTCs with Bitcoin Core 0.9.0, however the system no longer synchronizes and in the blockchain the balance is zero

As outlined in the comments, there's a couple of possibilities here:

1. You downloaded a very old version of Bitcoin Core, and managed to end up on a private chain where CPU mining is possible, and the chain is still new enough that the block reward is 50 BTC
2. The program you downloaded is a Bitcoin clone and gives the illusion of paying out 50 BTC or more, while either stealing crypto keys from other wallets on your computer, or later on asking you to pay some kind of recovery or unlock fee to claim these mined coins.

In either case, there is no Bitcoin. The block reward has not been 50 BTC for many, many years now (it was 12.5 BTC in 2019, and is currently 6.25 BTC in July 2020). Regardless of what method you used to mine, it is simply impossible to have a 50 BTC block reward dated in 2019 on the Bitcoin mainnet.

In short, you're either being scammed, or are mining on a private Bitcoin network with no relation to the public mainnet.

As Murch said in the comments below, you should definitely NOT use any address generated by this software to receive Bitcoin from an external wallet, exchange, or other service. All of these will send you real, mainnet Bitcoin.

As your version of Bitcoin Core is, at best, on a private network, you will not be able to access any externally received coins until you move your keys into a legitimate wallet that connects to the public Bitcoin network.

At worst, you're running some form of malware, and any real coins sent to addresses generated by this software will be stolen by whoever wrote it.