If you are here as a failed asylum seeker and you are being considered by the Home Office under legacy then for this, the life in the UK test will make no difference.
You are correct that for an application for long residence, you will need to show that you have passed the life in the UK test, however you simply need your passport to prove that it is you taking the test and not someone taking the test on your behalf. Therefore a certificate to return to the Ukraine from the Embassy, will not satisfy this unless it features a photograph of you, in which case you could try and provide alternative photographic proof for example, getting photographs certified as being a true likeness of you by a professional who has known you for a long time eg a doctor or solicitor.
If you contact the test centre and see what other evidence they would be willing to accept then you can try and proceed on this basis. If they refuse to let you take the test on the basis that you don't possess photographic proof, you could try and challenge this decision. Go and seek advice from a local solicitor about this.
I hope this answers your question in which case please accept. If you require anything further, please ask.
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