Well, you don't want to remove all the biologic substrate for your 10
gal filter at once. If you did, your 10
gal might go through another abbreviated cycle. However, taking some of the 10
gal biofilter substrate would accelerate the 55
gal cycle. If the 10
gal has a sponge for its biofilter substrate, you could snip a piece of it off and place it in the new filter, or squeeze it out onto the new filters biologic substrate (sponge?). Or place part of the 55
gal biologic substrate in the 10
gal filter for a week or two. Or even both- squeeze the 10
gal filter sponge into the larger filter, and put some substrate into the 10
gal filter that you can transfer in a week or two to boost the 55
gal biofilter later.
Your gravel in the 10
gal will also have the needed bacteria on it. Since it is easy to do, put some gravel in a pourous bag ( they sell them at
lfs) and drop it in the 55
gal tank. Take it out in a few weeks and put it back in the 10
gal.
It just occurred to me, are you going to transfer everyone out of the 10
gal into the 55
gal? if so, move the 10
gal filter, the plants and the fish over all at once. If no ammonia, nitirite after 2 or 3 weeks, start adding to the tank. Keep the little filter on the big tank, and if you ever set up the little tank again you just move the filter back and you are ready to go!