I assume you used snapshots, right?
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Hi! Snapshots store information only about the current state of the Spectrum, it does not know about the tape from which it was loaded and from where to continue loading. If the whole game fits in the Spectrum memory (like the first part of Neoplasma), so there is no problem with it. But if additional downloads from the tape are required, the game just doesn't know where to get them from.
So there are two options:
1) pass all three levels at once without using saves. then at the end of the game you can register a QR code on the site to record your progress in the record table.
2) at the end of each level you are given a password, with the help of which you can skip this level next time. but then there will be no QR code at the end of the game, because the password is too small to encrypt the progress of the skipped level in it.