I'm not a native speaker, but I tried to find an answer to this. I think "il est ici pour rester" means "he is here for a stay (but not permanently)". And "he/it is here to stay (permanently)" is "il est là pour rester". Can a native speaker confirm?
Here's a link with some examples: http://dictionary.reverso.net/english-french/here%20to%20stay
Pour is used with the infinitive to indicate purpose or aim. To reiterate what @Ariaflame said, one of the best things you can do for your French is to drop the idea that prepositions are always translated in isolation as some one thing, e.g. pour = for, dans = in, à = to etc. They often have to be considered in a grammatical context and cannot be translated well without that context.
For the record, that is a regional quirk. In most cases you should not have multiple prepositions next to each other in English. (Although there are exceptions. 'Near to' for example, which functions basically as if it was a single preposition.) But 'of to', 'for to', and so on are not used as standard, and would sound wrong to most.