Is it possible to obtain a key from connected database?

[little-brother]

I need a key to open a new connection or to attach a database in an another connection (that can be later than an original database was opened).

pragma key returns SQL logic error.
pragma <db alias>.key returns no row.

Or do I need to store the keys myself?

[utelle]

With pragma key='passphrase'; you can only set the passphrase to be used for encrypting and decrypting the database. That is, it is expected behaviour that PRAGMA key; (without a passphrase) fails.

The passphrase is never stored in the database itself. It is not even saved in memory, unless you use URI parameters with the database file name or you save it in your own application.

Therefore, it is the user's responsibility to provide the correct passphrase on opening an existing database file.

There is one exception,: the SQL command ATTACH. If the main database is encrypted then attaching another database to the main database connection via ATTACH without the KEY parameter assumes implicitly that the passphrase of the main database is valid for the attached database, too. If the passphrase of the attached database is not identical to that of the main database, then using the KEY parameter of the ATTACH command is mandatory. If the attached database is unencrypted, then specify an empty passphrase for the KEY parameter.

[little-brother]

Thanks a lot for the quick and detailed answer! :)
You saved my time by adding info about attacment database.