SATA III disk on motherboard with SATA I

Hello, My parents have pretty old computer - Intel Pentium 4 on ABIT IC-7 motherboard from year 2004. I want to buy a new HDD and I’m curious if motherboard will cooperate with SATA III HDD. Currently they have 320 GB Western Digital Green with SATA II and it’s working perfectly. Unfortunately, I was able to find only SATA III HDDs in stores. So my question is - will the SATA 3 HDD cooperate with SATA 1 controller on motherboard? SATA 2 works fine even without using the jumpers. Thanks a lot in advance.

Hi no sata 3 will only go to sata 2. sata 2 will go to sata 1 as you see.