Apply for H1-B transfer and extension together?

I am going to change job and do the H1-B transfer. But my current H1-B is going to expire in 3 month.

Some one told me that H1-B transfer only change the employer but keep the same expire date. If this is true, after I get my H1-B transfer done, I need to do H1-B extend immedinately, and have to pay all the fee again. Is this true? Thank you very much!