laughing like crazy here on the 32 inch rope you can wrap up both cages giggle only kidding...
ok no matter what your going to scare her when you go to move her thats unavoidable...so now what to do your thinking
ok here is what...place your hand ABOVE her head this should start to move her to the bottom of the cage cornering her... keep doing that and try it slowly at first till she gets to the bottom of the cage then just
go for it quickly and grab her and quickly put her in the other cage ...
she is going to try to squirt out from under your hand just keep that hand with spread fingers wide above her head...make sure while doing this the other doesnt fly out of the cage...giggle...that will be the hard part and the sooner you round her up the less stress for the both of you and your other bird too...so dont get all shy and squirmy on me now with this lol...hold her tightly enough so she dont wiggle out from your hand but not so tight you litterally suffocate or squish her..also if she is a female...she MAY just bite really hard IF this happens grit your teeth and bare it for the three second you will need to put her in the other cage...you will live thru this

if the other bird gets out...LEAVE IT ...dont chase after it...just make a note where it went...once you have the bird caught you want and transferred then SLOWLLLLLY get low if the escapee is low offer it a perch...with a extended hand it may fly again and have a crash and burn again when or if it does DONT rush to it just talk softly and let it get its breath for a couple minutes before approaching it again with the perch...when it gets on the perch stay as LOW as possible and walk really slowly back to the cage with the perch now held ...fairly ...close to you ..and simply when your near the cage extend the perch to the door and let it jump back in...
do this as often as it takes and BEFORE DOING ANY OF THIS AT ALL...make sure your room is safe ..no fans on...no standing water in the sink or toilet seat up...windows blocked doors locked...MIRRORS covered...no stove on...etc etc...no fly strips up...do a double check...then your good to go...

do the change of cage early in the day so she can settle into it all day long and let her without disturbing her again...so be sure your water and food is in there first.
ill want to hear about this adventure of yours...chuckle...but you will need to be sure to hang on if there is a bite and get her to the bottom of the cage cornering her fairly quickly before she figures out whats going on...
that cage is small so she wont be able to have many toys so be really selective on what you get....and hang them against the bars of the cage if they hang..a small cat ball with the bell inside is a good foot toy on the bottom...she will also take some time to go to the toys and most often they need to be shown HOW to use them and play so you have a bit of time to be VERY selective ...a swing would be nice also they like swings.
and when you can get a larger cage...be sure food cups are at the ends of perches...so they are not sitting in a food cup but just leaning into it to eat...a cuttle bone and mineral block are very essential also the NON FLAVORED kinds...and most pet stores dont sell the non flavored so here is a link to buy online...you will end up buying alot of things online so figure that one out if you need too.
here is two one for each bird cage and good price on both
http://www.ebay.com/itm/2-Calcium-Minera...=item337807cfe1these mineral blocks are even more important than calcium cuttle bone as they get calcium from these as well as other important minerals..again putting it near the end of a perch...
this site also sells plain cuttle bones and you would want the smaller ones...and this also shows a glass water fountain which is good because now they cant poop in their water and get feathers and crap in it contaminating the water..THESE you should be able to find in a pet store...the plain cuttle bones will be harder...there is on this site a minimum purchase order to escape a hefty ship cost but it yu get two of each it should work out.
https://www.birdsupplynh.com/catalog/pro...d65568e32246cd0