Don't have a "solution" per se, but a couple of questions.
Why are replacing the values, then pasting them back into the other sheet? I may not understand your needs, but that seems like an inefficient way to copy the data to another sheet. Are you wanting to copy that data to another sheet, then delete that data from the original sheet?
Also, perhaps it is a typo, but in your second line of code, should that be?
Code:
Lastrow = range("A1").end(xldown).row
Myrange = "AB1:AB" & Lastrow
Normally if you select something, then do something with the selection you can omit the selection, so instead of:
range(Myrange).specialcells(xlcelltypeblanks).enti rerow.select
selection.copy
Replace it with:
range(Myrange).specialcells(xlcelltypeblanks).enti rerow.copy
Finally, it is not always necessary to select something to do something with the range/object. Selection slows the process.