We consider a fluid-structure interaction (FSI) problem discretized by finite elements featuring two different grids that do not necessarily agree on the interface separating the computational domain of the fluid from the one of the structure. After identifying a master domain (the structural domain) and a slave domain (the fluid domain), we build up two Radial Basis Function (RBF) inter-grid operators, one Pfs from master to slave, and the other Psf from slave to master. Then, we enforce the kinematic condition by equating the fluid velocity at the interface as the image through Pfs of the temporal derivative of the structural displacement. On the other hand, the dynamic interface condition is fulfilled via a variational method where the strong form of the structural normal stress is obtained as the image through Psf of the strong form of the fluid normal stress. A numerical verification is carried out for a straight cylinder and for a patient-specific arterial bypass geometry. This new method is easy to implement and optimally accurate.