No, I got that you wanted to use a computer PSU. The only thing there is I thought that the maximum amps put out by one of the connectors was 5A at 12V.
That adapter board won't work I'm afraid. That's for chargers like
THIS one that don't have balance ports built into the side, but an adapter port to use different boards for different batteries.
The charger you've picked has one of those 'boards' built in, so you cannot use another board without rewiring the batteries to have JST plugs.
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The white block on the side of the charger is the balance 'board', but there is no port for other balancing boards to be used.
Having seen the power output of the charger (50W), the PSU should be able to provide enough power: 5A * 12V = 60W. Multiply this by the % efficiency (say 80% - most higher quality chargers are 85% so this is a conservative estimate), so 60W * 0.80 = 48W, so it barely limits the charger.
The reason I said it would limit the charger is that I use chargers with 180W charging capabilities, so it would definately not be enough for me.