Hi Rosov Aulmais,
you can read all about the Suspect Timer and the Criminal Timer aswell as find information on the Command Burst (Boost) on the EVE Help Center website.
The short version is as Qia Kare said, Boost only gives you a limited Weapon Timer and will not transfer Suspect/Criminal timer. To my knowledge the only modules that transfers such timers are; Remote Cap Transfer, Remote Shield/Armor/Hull transfer aswell as the other Remote assistance modules (Remote sensor booster, Remote tracking computer…)