請教皮匠老師及各位：這樣身份有問題嗎

2月底被lay off (H-1B在2009年expire), 但是在1月份已經找到新的公司，並且新公司已經在2月初申請了新的H-1B，現已經收到新的receipt ( 但是starting date是6月1日)。問題是被lay off( 2月底)到新的上班時間(6月1日)中間會不會有Gap的問題？新公司的律師說沒有關係。他引用了H-1B portability rules: "a person in H-1B status may commence new employment upon the filing of new petition by the prospective employer if: (1) s/he was lawfully admitted; (2) the new petition is nonfrivolous; (3) the new petition was filed before the date of expiration of the period of stay authorized by the AG of the H-1B beneficiary; and (4) subsequent to such lawful admission the H-1B beneficiary has not been employed without authorization before the filing of such petition."公司的律師對嗎？謝謝！