As to the UK, the general rule is to try to achieve 30 years of UK NI "stamps" (i.e. contributions) credit. With good strategy you can get years of credit free & gratis or at low cost. Or you can buy Class 3 pension years (up to 6 years after the relevant year
http://www.hmrc.gov.uk/manuals/nimmanual/NIM25025.htm )
See, generally:
https://en.wikipedia.org/wiki/Nation...urance#Class_3
(There is a new Class 3A voluntary scheme this year useful for certain persons
https://www.gov.uk/government/upload...tted_FINAL.pdf )
It is often possible to pay Class 2 contributions at a much lower rate; or, through a friendly employer, Class 1 free or at low cost.
The Swiss AVS system generally does not allow even a Swiss citizen to contribute voluntarily while living in an EU/EEA country. (Those who do contribute while abroad, mainly Swiss citizens, are sometimes blindsided by the inclusion of a wealth calculation in the contribution amount.) As for NI, in my experience, HMRC and the Department for Work and Pensions do not have such a residency criterion and often do not enforce nationality rules even when they apply.
Most national state pension schemes are skewed to benefit the low-paid and only some limit benefits to prevent "unjust enrichment". (The USA does so through its "Windfall Elimination Provision" and Canada by having a means- and residence-tested Old Age Security scheme alongside the CPP/QPP.)
For private pensions and supplementary schemes (including tax-sparing saving schemes such as ISAs in the UK) you need to take account of future residence expectations and relevant tax treaties. Thus: the USA has an exemption from its very nasty PFIC rules for pension schemes with certain countries (US-UK Tax Treaty, art. 19) and with many countries exempts pensions from double taxation (taxation by one country on internal gains and earnings, and in the other when benefits are received). But the Internet is full of horror stories of pensions schemes and trusts in one country, and alimony, divorce settlements and wealth taxes in another.
Most of what I have written may not be relevant to the issue you raised. But you never know. State pension systems can be gamed. Government schemes for civil-service and military retirees tend to be protected in any case. But private and voluntary nongovernmental schemes are often targets for "advisors" who do not have your interests at heart and/or do not know the intricacies of cross-border eligibility and taxation.
State schemes are often subject to totalization treaties: these provide that contributions for less than the minimum period (for the USA and the UK, ten years) will be credited to the other country's scheme (unless you contributed to both during a particular year). The treaties also relieve most workers from double liability for contributions (unless waived, which some US employers needed to do to maintain company-wide schemes). A totalization treaty may also protect your Cost of Living Adjustments (the UK denies COLAs to its retirees in countries outside the EU/EEA/Switzerland except for the USA (which otherwise threatened the UK with draconian retaliation, something Canada should have copied, but didn't).
Your friend should educate him/herself as much as possible for free on the Internet and from books before seeing an accredited independent financial advisor. Who may, or may not, understand all the cross-border implications.