Power supply 5Volt 1 Amp

[#1]

I have a simple security camera with a screen.  The power supply has burnt out.  It is 5 Volt 1 Amp with 3.5mm plug.  I have an old  power supply which is 5 Volt 2 Amp with 3.5mm plug.  Will that work o.k. ?  I am assuming that the screen will only draw 1 Amp and that the fact it is 2 Amp will make no difference. 

The system also has 3 x separate cameras which  all use the same type of power supply, and I was thinking it might be better to use one of those power supplies for the screen and keep the 2 Amp variety for that camera.  I am out of my depth here !

Any advice would be appreciated.

[#2]

@shermans 

You've said the voltage and plug are the same, so your 2A power supply will be fine to replace the failed 1A one.  The device will only draw the same current as before, and the power supply will be under less stress than the original.

[#3]

As @RobPN says, no problem with the power drawn, as long as the polarity is the same.

Are the units marked, or can you test for polarity if they're not?