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
I would strongly recommend speaking with your advisor as a first step. He may be able to initiate collaboration between you and the researcher running the other lab while you're still performing your PhD work, allowing you to kill two birds with one stone.
If this is impractical for any reason, I would recommend reaching that, as soon as you think you have a strong enough knowledge base to be able to demonstrate expertise in your field, you should reach out to the professor at the second lab and express your interest. Research grants often take many months, and demonstrating your interest in his work at an early stage may give the professor more interest in writing a grant in which you could participate. Note that I would definitely recommend waiting until you can impress the professor with your knowledge. Postdocs are hired to get stuff done. While it's true you still are a PhD student, you're essentially applying for a position as a postdoc, and if you're not an expert (or close to one) in your field, he will likely be wary about bringing you in to your lab.
This last reason is why people typically wait until they're pretty far along, if not outright finished, with their graduate work before looking for postdoc positions.