The squeezing transfer from a squeezed vacuum injected in one cavity to the output spectrum of the other cavity in an optomechanical system is investigated. By calculating the noise spectrum of the output field, it is found that two squeezing dips appear symmetrically located about the resonant point. Besides the contribution from the destructive interference between the noise fluctuation of the input field and its optomechanically modified one, the major part of the squeezing is transferred from the squeezed vacuum injected in the cavity. Additionally, it is shown that the adverse effects of the environment temperature on the output spectrum can be strongly suppressed by the injected squeezed field. This study can be useful in quantum communications via the optomechanical interface.