The painting was a [...] copy of the original.
Are there other common expressions other than exact and identical?
Other words and phrases (from the top of my head)
Clone (for persons)
Doppelgänger (also for persons)
Edit: sorry, most of these don't match your question. Perhaps only 'duplicate', but for other uses I will still keep them here.
- Identically copied from an original.
So the sentence would be
The painting was a duplicate.
You could also try "a facsimile of the original".
From wikipedia: "A replica is an exact reproduction, such as of a painting, as it was executed by the original artist or a copy or reproduction..."
It would make more sense to say the painting was a forgery.
Art forgery is the creating and selling of works of art which are falsely credited to other, usually more famous, artists. Art forgery can be extremely lucrative, but modern dating and analysis techniques have made the identification of forged artwork much simpler.
forge (verb) 3. Produce a fraudulent copy or imitation of (a document, signature, banknote, or work of art): the signature on the cheque was forged
Finally, since no one else has suggested this, if the OP wishes to keep his original sentence then the terms, perfect, or imitation could both fit.
The painting was a perfect copy of the original.
The painting was an (a perfect/poor) imitation of the original