How to get lab resources back from a post-doc who resigned while on vacation and not coming back? I am posting this on behalf of my advisor.

A post-doc in my research group at US told that he'd be going home to meet his family who are in a different country, but after two months he emails that he is quitting. He has the laptop which my advisor paid for and important research data. He hasn't communicated in email that he will return the things he owes. Besides, he was playing tricks by procrastinating his return, even confirming his return tickets, only to finally resign.

What are the legal ways to get the resources as well as the monetary compensation made in his absence back, in case he doesn't respond?

(Note: The research data needs to be surrendered because it belongs to unpublished work from other groups, not because it wasn't backed up.)
The issues you are describing of misappropriation of university equipment, research data and unearned salary, rise to a level of seriousness that a rank and file faculty member is not equipped to deal with and will not typically be expected to deal with. It is time to call in the cavalry — by which I mean, the matter should be referred (probably through your advisor’s department chair) to the university legal counsel or similar office. They will take appropriate steps, starting with sending the absconding postdoc a threatening letter, and ending with who knows what (in theory, a police report and/or civil lawsuit, although given the negligible economic value of the misappropriated items and the difficulty of proving outright theft, I’m guessing not much legal action will come of the whole business).

Of course, I’m hoping that the postdoc will listen to reason and return what he has wrongfully taken, but in any case, if your advisor hands the matter over to the university authorities, and cooperates with the resulting follow-up actions, then even if the items are not returned, your advisor will be in a good position to explain to their funding agency and collaborators that they tried in good faith to fix the problem, and the embarrassment and damage to their professional relationships will be kept to a (probably negligible) minimum.

Good luck!