Despite the increasing number of species invasions, the factors driving invasiveness are still under debate. This is particularly the case for “invisible” invasions by aquatic microbial species. Since in many cases only a few individuals or propagules enter a new habitat, their genetic variation is low and might limit their invasion success, known as the genetic bottleneck. Thus, a key question is, how genetic identity and diversity of invading species influences their invasion success and, subsequently, affect the resident community. We conducted invader-addition experiments using genetically different strains of the globally invasive, aquatic cyanobacterium Raphidiopsis raciborskii (formerly: Cylindrospermopsis raciborskii) to determine the role of invader identity and genetic diversity (strain richness) at four levels of herbivory. We tested the invasion success of solitary single strain invasions against the invader genetic diversity, which was experimentally increased up to ten strains (multi-strain populations). By using amplicon sequencing we determined the strain-specific invasion success in the multi-strain treatments and compared those with the success of these strains in the single-strain treatments. Furthermore, we tested for the invasion success under different herbivore pressures. We showed that high grazing pressure by a generalist herbivore prevented invasion, whereas a specialist herbivore enabled coexistence of consumer and invader. We found a weak effect of diversity on invasion success only under highly competitive conditions. When invasions were successful, the magnitude of this success was strain-specific and consistent among invasions performed with single-strain or multi-strain populations. A strain-specific effect was also observed on the resident phytoplankton community composition, highlighting the strong role of invader genetic identity. Our results point to a strong effect of the genetic identity on the invasion success under low predation pressure. The genetic diversity of the invader population, however, had little effect on invasion success in our study, in contrast to most previous findings. Instead, it is the interaction between the consumer abundance and type together with the strain identity of the invader that defined invasion success. This study underlines the importance of strain choice in invasion research and in ecological studies in general.