Can wallet created from Bitcoin core be transferred to an Android device? I worry that if I install a wallet in my Phone, it would have a different wallet from the one I created in PC.
Even if it is NOT recommended (especially if you want to store a considerably amount of funds), it is possible to share a "wallet", or more specifically a Private Key, from one wallet app to the other. Bitcoin wallets are just keychains, they only contain keys, you can have the same private key in both apps.

It is not recommended because it's more likely that you can get your phone stolen than your computer, especially if it's not a laptop but a desktop computer, also mobile wallet code and mode (light wallet or SPV vs full-node) can be weaker. Sharing private keys means that who first gets the access to the wallet or the key directly can spend the funds.



Here's how to share it anyway:

You can easily export your private key using the dumpprivatekey command from Bitcoin Core (here's how to export it on Bitcoin Core GUI, or bitcoin-qt, if you don't have the qt version you need to launch the command via bitcoin-cli and enter the same commands)

Then you can take any Mobile wallet with import private key capability like Mycelium (Android) or BreadWallet (iOS) and import it via their "import private key" feature.

In Mycelium, to import a private key, you have to click the hamburger button, then select "Cold storage" and then Clipboard (you need to securely send your private key from your computer to your phone, this usually means no email and no standard IMs, the safest way is to transcribe it manually). Also note that you need to password protect your wallet (preferably with a strong password) or users that can access your phone will be able to spend your funds, Mycelium will warn you if you don't do it.



Also note that bitcoin-qt and Bitcoin Core don't use HD or BIP32, this means that you get less anonymity if you reuse the same address or if you don't import a large number of keys, to have multiple "change" addresses available in both wallets.