Advice on emigrating abroad and UK pension?

I am in the process of persuading my mother to emigrate abroad from the UK. My wife, children and I are already living/working abroad. However, what I want to find out is as somebody who has lived in the UK all her life, is she entitled to receive the UK state pension as she paid all her taxes. Secondly, as her husband ped away a few years back, would she be entitled to claim his pension or a percentage of his pension to? Any advice or pointers would be greatly appreciated.