Advice for Adding Flexible Supply to Existing Faucet

[lowlight21]

New to the forum with a DIY question. I am in the middle of installing a Watts recirculating pump in my house which requires the installation of a new check valve (link to valve) at the sink furthest from my water heater. My sink plumbing is all copper, including a 3/8 soft copper riser from the shutoff valve to the faucet (I believe this copper line is physically part of the faucet so I can't easily replace the supply line). I would like to incorporate flexible lines between this existing soft copper supply line and the check valve. Can I just use a flex line with a 3/8 compression to put a flex line in between this copper and the new check valve? Am I missing an obviously better/easier idea? Thanks in advance for any assistance here!

P.S. I am first replacing these two shutoff valves that are leaking, and will then address installation of the check valve and making the supply line connections.

My existing undersink plumbing:

Sample of how the check valve is plumbed:

 

[Jeff H Young]

Bottom picture is a good guide that looks like a good way to go.

 

[Sponsor]

 

[Breplum]

that device is not a check valve by the way. in fact it mixes hot and cold so your water will be very warm/hot when you first open the tap.