Cut & paste selected cells, by pressing button, to first blank row in table

Hi,

My excel skills sort of ends at (simple) functions, pivot tables and recording macros and since I can't seem fix this issue with this limited excel skillset I'm in need of help.

I've attached a sample workbook that doesn't look exactly as the original one but it resembles it and I hope that's enough to help me out.

Anyways, what I want to do is this:
1. Select one or several rows (always a full row, that is, from column A to D) in sheet1. For example selecting A2:D2.
2. Press "Archive"
3. By pressing Archive the selected data is cut and pasted to same columns in sheet 2 as well as placed in the blank rows in that sheet.

I've tried solving this by creating a macro but I either get an error or it (the macro) keep replacing my previous addition to the table when I press the macro.

I want to solve this as simple as possible because neither me or the users it's designed for have the skills to work out any furher issues nor do we need for more sophisticated
solution than this.

Hope I've provided all necessary information.

//Ejb123Erok

Thank you Sixthsense and Andy for the quick responses.

Just one question for you each:
Sixthsense: The code cut and paste the rows but it moves everything, not just he selected row.

Andy: it just copies, what changes to the code to I need to do so that it removes it from sheet one (i.e. cuts and pastes the selected row).

Sub MoveDataOnClick()
Dim LR&,  ms As Worksheet
Application.ScreenUpdating = False
Set ms = Sheets("Sheet2")
With Sheets("Sheet1")
    LR = .Cells.Find("*", , , , xlByRows, xlPrevious).Row
    .Range("A2:D" & LR).Cut ms.Cells(Rows.Count, "A").End(xlUp).Offset(1)
End With
Set ms = Nothing
Application.ScreenUpdating = True
End Sub

Many thanks for all the help this far. Before I put this a a "solved" issue I have a few additional things on the same workbook I would like to have some help with.
Note: I'm using AndyLich's coding for the archive-button since I tried it first and it worked fine.

Anyhow, when I archive one or several selected rows I want the archived row(s) to be deleted from sheet1, not just the content, because a user might want to archive any row and not necessary the first or last one, thus I don't want empty rows in the middle of the table.

Furthermore, if possible, it would be great if the archive (sheet2) was protected from any editing. However, If I protect the sheet the archive-button doesn't work (obviously). Is it possible to incorporate that into the buttons coding so when pressing "archive" the archive sheet2 gets temporarily unprotected during the "cut and paste" process.

I feels like I'm making someone else do my job but I really can't do this on my own!

Sorry for bumping but I think this thread has been forgotten and I still have issues with what was brought up in my last post. If anything was unclear with it I'm happy to explain in more detail regarding what I was requesting help.