Access to the wallet through a private key

The official Algorand Wallet does not support importing a private key.

Command line tools do.
See algokey and How to recover my wallet with 24 word mnemonic - #6 by fabrice

Disclaimer : Typing passphrases and private keys on a computer may open you to attacks that are not possible on the Coinomi hardware. Algorand makes no representations regarding the functioning or security of third party wallets, exchanges, or tools mentioned in the answer above, and disclaims any liability therefor. You are fully responsible for the security and the availability of your keys.