My old notebook has the following inside: Intel Core i5-3210M CPU 2.5GHz with 8GB RAM, an Intel HD Graphics 4000 and GeForce GT 635 M.
That is unfortunately broken now.
I was now offered a notebook with Intel Core i3-7130U CPU 2.7GHz with 8GB RAM and an Intel Graphics 620.
Is that really better or at least equivalent?
Well there's the iGPU weaker Cpu I do not know grad and Ram is the same so get it rather weaker unless the thing has a SSD and yours not
So without a model of the i3 you can't say.
The HDGraphics 620 are better than your graphics card, but the CPU is probably worse.
If he is without SSD, then leave it.
Which budget?
Are both almost exactly the same fast, only the graphics are better on the i3 (is probably the 7100U). If you want to get it right, get one with Ryzen 3 or 5
I correct myself the GPU is weaker
