How to replace an empty cell with the data of the one above

Hello,
I'm a newbee on the forum and a medium excel user without VBA programming knowledge.
Currently I am stuck with the folowing challenge, is there anyone who can help?

Challenge:
I'm working on a file (datadump) which looks like this.

Knipsel.PNG

Colomn B contains clientnumbers. I need to replace the empty cells with the data (clientnumber) of the one above.
Manualy I copy the cell above the empty one and paste its content in the empty ones untill I reach another one containing a clientnumber.

When I recorded this procedure (I used the searchwindow, searched for an empty cell, clicked the one above and pasted as mentioned above).
The recording doesn't give a code I can use for whole my file. The code looks like this.

Knipsel2.PNG

Is there anyone who can help me out with a code that works for whole my file?

Thanks in advance!

Lenny

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Wow, Jindon you're brilliant!

The code worked perfect for the A colomn. Al I had to do is change "a1" to "b1" and now it works fine for my file.

Thank you so much, this will save me tons of time!

Lenny