Respiratory motion is a source of artifacts in multimodality imaging such as PET/MR. Solutions include retrospective or prospective gating. They have however found limited use in clinical practice, since their increased overall acquisition duration to maintain overall image quality. More elaborate methods consist of using 4D MR datasets to extract spatial deformations in order to correct for the respiratory motion in PET. The main drawbacks of such approaches is the relatively long acquisition times associated with 4D MR imaging which is often incompatible with clinical PET/MR protocols. The objective of this work was to overcome these limitations by exploiting a generalized reconstruction by inversion of coupled systems (GRICS) approach. The methodology is based on a joint estimation of motion during the MR image reconstruction process, providing internal structure motion and associated deformation matrices for retrospective use in PET respiratory motion correction. This method was first validated on four MR volunteers and two PET/MR patient datasets by comparing GRICS generated MR images to 4D MR series obtained by retrospective gating. In a second step 4D PET datasets corresponding to acquired 4D MR images were simulated using the GATE Monte Carlo simulation platform. GRICS generated deformation matrices were subsequently used to correct respiratory motion in comparison to the 4D MR image based deformations both for the simulated and the two 4D PET/MR patient datasets. Results confirm that GRICS synchronized MR images correlate well with the acquired 4D MR series. Similarly, the use of GRICS for respiratory motion correction allows an equivalent percentage improvement on lesion contrast, position and size, considering the PET simulated tumors as well as PET real tumors. This work demonstrates the potential interest of using GRICS for PET respiratory motion correction in combined PET/MR using shorter duration acquisitions without the need for 4D MRI and associated specific MR sequences.