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From an inelastic excitation and breakup experiment with a Be beam at 29 MeV/u, a large He+He cluster decay width of 1.1(2) MeV is determined for a state at an excitation energy of 10.3 MeV and with a spin parity of 0+. By using the R-matrix analysis, a cluster spectroscopic factor of 0.53(10) is extracted from the cluster partial width, providing a strong support for the clustering structure in Be. A specially designed zero-degree telescope played an essential role in the present experiment and has been demonstrated to be a promising tool in future studies of the molecular-like resonances near the cluster separation threshold. [ABSTRACT FROM AUTHOR]