Can an Employer convert from an existing 403b plan (variable annuity) and transfer all assets to a new employer sponsored 401k plan?
403b plans are used by school districts, colleges and universities, nonprofit hospitals, charitable foundations and the like for their employees while 401k plans are used by most everybody else. I would suspect that a school district etc can use a 401k plan instead of a 403b plan if it chooses to do so, but the reverse direction is most likely forbidden: a (for-profit) company cannot use a 403b plan. One difference between a 403b plan and a 401k plan is that the employer can choose to offer, and the employee can choose to purchase, stock in the company inside the 401k plan. This option obviously is not available to charities etc. which don't issue stock.
Your comment that the 403b plan invests solely in (variable) annuities suggests that the plan administrator is an insurance company and that the employer is moving to more "modern" version that allows investments in mutual funds and the like. Forty years ago, my 403b plan was like that; the only investment choice was an annuity, but some time in the 1980s, the investment choices were broadened to include mutual funds (possibly because the 1986 Tax Reform Act changed the rules governing 403b plans). So, are you sure that your employer is changing from a 403b plan to a 401k plan, or is it just a change of 403b plan administrator from the insurance company to another administrator who offers investment choices other than an annuity? Note, of course, that insurance companies have changed their options too. For example, TIAA (the Teachers' Insurance and Annuity Association) which was the 403b plan administrator for many schools and colleges became TIAA/CREF (College Retirement Equities Fund) where the CREF mutual funds actually were pretty good investments.