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Will it be possible to calculate the ABV of some sloe wine that I've brewed, if I measured the gravity, needed to add a known amount of sugar solution, and then measured the gravity at the end of fermentation?

I started with 4600mL of sloe wine, which had an original gravity of 1095. It went into a demijohn with an airlock, and continued to ferment. When it was done, I racked it into a demijohn that was 5000mL to clear, and had to top it up with some sugar solution (1 part sugar boiled in 3 parts water). I didn't measure the gravity at this point. After a couple of months it was clear enough to bottle, and I measured the gravity as 1005 at this point.

If I know the volume and could find out the gravity of the sugar solution, will it be possible to work out the ABV of final wine?

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A gravity reading is derived from the differences in gravity between where fermentation started (OG), and where it ended(FG).

Unfortunately, you need both numbers to get an accurate gravity reading. The good news is, you now have a reason for some friends to come by and play "guess the gravity".

I believe the best way to handle the situation next time is:

A) gravity reading before primary fermentation
B) gravity reading after primary fermentation
C) gravity reading after adding sugar solution (secondary ferment)
D) gravity reading after secondary fermentation

Instead of using A for your OG, you would add to it, the difference of C - D. This is your new OG.

B and D will most likely be the same value so use that as you FG. If they are not (yeast stressed, old, etc) you can adjust your FG similar to how the OG was adjusted.

Also, if using a refractmeter for taking gravity, there is a correction factor you need to figure in once alcohol is present in the solution. This is the case for beer, I'm not sure about wine. Probably the same principle: https://www.brewersfriend.com/how-to-determine-your-refractometers-wort-correction-factor/

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