No, no adapter can convert to what you want to see. The two lighting systems (plain RGB you have, and ARGB) are quite different and cannot be mixed on one header. Because of the designs, a plain RGB system (you have) can only make an entire strip one colour at a time, although that colour can be changed. It cannot do a wave moving down the strip, or a rainbow. An ARGB system can do that. You can get a special lighting Hub that allows you to input control signals from a plain RGB system and convert that to output to drive an ARGB light set. However, the signal that the plain RGB system can provide to that converter can NOT include any of the complex things an ARGB light set can do. So when you do this, the ARGB lights can only display the SAME more limited patterns that the plain RGB lighting system can do.
To do what you want, you need a set of ARGB lights AND a controller box for them that operates independent of the mobo. SOME of these systems actually allow you to connect the controller box to a mobo USB2 header so you can use a software utility supplied to control the lights.