Time-localized projectors in string field theory with an E -field

We extend the analysis of Bonora et al. [hep-th/0409063] to the case of a constant electric field turned on the world volume and on a transverse direction of a D-brane. We show that time localization is still obtained by inverting the discrete eigenvalues of the lump solution. The lifetime of the unstable soliton is shown to depend on two free parameters: the b parameter and the value of the electric field. As a by-product, we construct the normalized diagonal basis of the star algebra in the B{sub {mu}}{sub {nu}}-field background.