Let's assume that there is an immigrant whose resident/host country is US which has low inflation while his home country has high inflation. The immigrant invests in his home country using his earnings from his host country. From the point of view of the immigrant when he returns to his home country after a period of say 10 years, will his investment be have been affected by the home country's inflation rate or the destination country's inflation rate?
His investment in the home country would be affected by the home country inflation rates, since it probably would be made in his home currency (let's call it H$) - so if he invested 1000 H$ 10 years ago and now has 2000 H$, he may be able to buy less for these money (in his home country) than before.
Also he may be influenced by the exchange rate - i.e. how many H$ one gets for his US$, since I assume he is paid in US$, but in his home country he would probably invest in H$. If inflation is high in his home country, his assets in H$ may depreciate quickly and cost less than if he kept them in US$. But this rate is affected by both inflation rates, and exchange rates can be influenced by other factors too.