L1B to H4 to file H1B with a Status of H4

[Jana J]

My wife is currently on L1B visa valid till June 2017. After that she would be on H4 so that she can continue in US. I am planning to apply H1B visa for her this year and we found an employer willing to sponsor H1b. However, the employer wants us to file for H4 (effective date of Mar 25th)immediately so that they can file for her H1 with a Cos from H4 to H1. Also, they want her to stop working on L1B so that she would be on H4 Pending status before 1st April. They want to avoid a situation where there would be a change of status during the H1B application process. 
1. Is this valid? 
2. If she stops working on L1B and with H4 not yet approved, what would be her Status in the interim? 3. Would it be legal to stay in the US in the interim?