the metal pads on the replacement screen should take the solder easily when heated.
note: make sure that your soldering iron has heating up completely before attempting. test this out by applying the end of the soldering wire to your iron to ensure that it melts quickly.
step one:
apply the tip of the soldering iron to one of the pads and then "feed" the solder to the point where the soldering iron tip is making contact with the metal pad until you have a blob about 1.5-2mm in size.
step two:
repeat step one for the remaining 3 pads so that you now have 4 "dots" of solder on the pads.
step three:
apply the soldering iron tip to a pad where the solder meets the pad until the applied solder pools (melts again) and then, taking the leads from the speakers one at a time, "feed" the bare wire into the center of the melted dot and remove the soldering iron, taking care not to move or shift the speaker wire while the solder cools (this only takes a second).
examine the solidified solder. it should still have a shininess too it. if the solder appears extremely dull, re-flow it with the soldering iron and then let it cool again. this ensures a good solder connection opposed to what's termed as a "cold" solder joint (the extremely dull coloured ones) which can break or cause connectivity issues.
note: be sure to apply heat for only the necessary amount of time otherwise you risk melting the pads from the flexible ribbon cable.
2nd note: make sure that you connect the wires correctly as shown in the image below: