Can you move someone else's Jenga piece (properly placed in center position) at the top of stack before placing your piece? Husband moved wife's piece in attempt to not lose.
If the block was properly placed
That's not legal.
It's not legal to move a block from an incomplete top row.
It's not legal to move a block from the topmost complete row.
In fact, if you start moving a block other than the one you move to the top, you must put it back into its original position before continuing.
You can touch other blocks to find a loose one — but if you move a block out of place, you must fix it (using one hand only) before touching another block.
If the block wasn't properly placed
Although not stated in the underspecified rules, it's the responsibility of the player placing the block to place the block on the top layer according to the same pattern used during setup.
If they were moving it from say the centre position to the left or right side, then absolutely not, if they were fixing it because it was placed improperly, IE overhanging the edge, off-centre, that's acceptable.
HOWEVER doing this is a risk to you, since it was you who would make the tower fall, what you should do is have your opponent fix the piece they placed before starting your turn, that way if they make it fall, they lose, not you.