No.  You must purchase an upgrade to Professional on the machine that came with Basic.
sir, i purchased two dell laptops with genuine Dell oem windows 7.One laptop came with windows 7 home basic 64 bit and other came with windows 7 professional 64 bit.Now i want to upgrade windows 7 home basic to windows 7 professional so can i use my dell windows 7 professional oem key for this  purpose. So after upgrading laptop  which have operating system windows 7 home basic to professional will this work correctly. Will both laptops can be activated with same windows 7 professional oem product key. thanks  for watching.
About upgrading windows 7 home basic to professional.