How to "cultivate" a postdoc position during PhD program? Imagine you're a PhD student, and you found a research group, in another university, that you'd like to join for a PostDoc period. 

You want to join that group because you really like their subjects, and their projects, and/or for other reasons. You just dediced you would like to join them.

Now, what could you do during your PhD to augment the probabilities to reach this objective?

You might say: just relax, make an awesome work, and then, when you're ending your doctoral period, contact that group PI and ask to be hired (we already discussed how to cope with this phase).

Okay, but, is there something you could do during your PhD before that moment?

What could you do?

Keep up-to-date on their scientific papers?

Email them? About what?
Visit their lab?

Thanks a lot
You want to establish substantial professional contact with the head of your target group long before your doctoral period is about to end.  They need to know who you are already when your postdoc application crosses their desk.  It is never too early to start.  Here are a few suggestions.


Ask your advisor to invite the head of the group to give a talk in your department.  Meet with them one-on-one.  Ask about the possibility of a short visit to their lab to give a reciprocal talk.  (Prerequisite: Have something compelling to talk about; be a good speaker.)
Ask about the possibility of summer internships.  (Prerequisite: Be a good candidate for a summer internship.)
Ask your advisor to suggest a one-semester student swap.  (Prerequisite: Be someone that the other person would want to hire as an RA.)  More generally: Convince your advisor to collaborate with the other group.
Ask the head of the group to be an external member of your dissertation committee.  Ask at least two years before your defense. (Prerequisite: Have a thesis topic that they will care about.)
Talk to the head of the group and/or his students at conferences.  Join them for lunch, or dinner, or coffee, or beer, or whatever.  (Prerequisite: Be an interesting human being.  Know a few good places to get lunch/dinner/coffee/beer/whatever.)
Don't put all your eggs in one basket.  Cultivate multiple colleagues.  Some may develop into future employers, others into future research collaborators, still others into letter-writers, still others into mentors,  perhaps a few into friends, and most into nothing.  (Prerequisite: Know more than one person.)
Most importantly, don't think of this process primarily as "cultivating a postdoc position".  Think of it as cultivating a research community.  People will notice if your motivations are mercenary, if only subconsciously.