Based on these specs, its not the best amplifier out there but its also far from the worst. I wish I could see how Onkyo rates it into 4 ohms. How much are you thinking of paying for this?
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Those specifications look quite decent to me; of course without an audition it's always hard to say but I see enough here to put it on a short list, and since he already owns it for a total cost of $0, I see no reason not to run it.
Power: 150 watts 8 ohms 0.09% THD, IMD, spec'd via the FTC method ... all good so far.
Damping factor 8 ohms of 40 means modest amounts of Global Negative Feedback ... you would get DF numbers in the hundreds if excessive GNF were used, and since minimal GNF almost always points to good overall sound quality, nothing to fear here either.
Wideband frequency response ... always a plus in my experience. Onkyo specs 5 to 100K within 1 DB, an excellent figure that points to a wide power bandwidth (read: excellent bass).
100dB s/n ratio ... when you get into three figures here, excellent result and should be very low noise circuit.
As for no 4 ohm rating, since Onkyo is rating via FTC, what probably is happening is the amp went into protection mode during the pre-conditioning phase, which is a reasonably tough condition to meet. You cannot measure the amp until it has endured 1 hour of pre-conditioning.
Note that if any amp cannot pass the 1 hour @ ⅓ power continuous without going into protection, FTC rules state you cannot provide a 4 ohm rating even if the amp has no trouble playing music into that impedance load (which will be much less than ⅓ continuous power). Doesn't scare me.
Since he already has a phono preamp built into his record player, and only needs 1 source input, I'd go with a simple volume control and be done with it. The Emotiva Control Freak is $50, no active components to add noise, and even comes with cables.
Done.