Need advice regarding a present for record-playing lover : should I upgrade his amplifier or his speakers first?

Hi. My partner is moving in with me in a few months and so will have to leave behind his buddy and their shared audio setup for the record player. Earlier this year he got this home theather sound system, Sony DAV 2006 Dream System (4 speakers and amplifier console), for 100 bucks from a friend getting rid of it, but admitted it was far from ideal for playing music. (He's not using it atm)

I also love listening to vinyls with him and have a sensitive ear to good quality sound but I don't know much at all about equipment. He's on a tight budget for a few years now that he just finished his education, and I have a little budget to invest in his passion this Christmas although not a thousand $

So I was wondering which would make the most difference to replace first (and I guess either him or I as a gift will replace the rest another year) , considering what he's got now and its capacity? The speakers, or the amplifier console? I saw the console doesn't seem to have much settings buttons to play with regarding sound balance...

This question alone being answered would help me a lot! But if you could also give me recs for specs or models I could look into, I'd be truly delighted. (~500$ budget)

I would prefer to buy used to get the best quality for my buck, but I'll be dependent on what's available on the local or online used market.

Thank you very much!