We present an analysis of spatial and temporal spectra of the observations of scintillations in a laser beam (532 nm, ∼200 mW power) traveling along a 144 km path at an altitude of 2-2.4 km above sea level, just above the atmospheric boundary layer, between the islands of La Palma and Tenerife. The observations were performed during nighttime on July 18 and 21, 2011, by means of a telescope with an aperture diameter of 1 m. Strong scintillations were observed. We compared the temporal and spatial spectra of the scintillations. For the temporal spectra, we performed the correction for the aliasing effect due to the low frame rate. The 2D spatial spectra of the scintillations in the observation plane were found to be close to isotropic. This allowed for transforming them into 1D spectra. We found a good agreement between the temporal and 1D spatial spectra. This corroborates the applicability of the Taylor hypothesis of frozen turbulence for finite-size laser beams and strong scintillations.