There are no scenarios that allow you to reuse any of the THWN wire that is in the conduit now. It is just too short, since as you say it is spliced immediately upon entering the house.
Trying to establish a splice point at the old location will be rather difficult and not worth doing given the low cost of wire. Since you want to go the last 10 feet in direct burial wire, you will need to bury at 24" which means actually 14', and the descent to 2' depth at both ends also needs to be in conduit solely as wire physical protection. To say this is ungainly is an understatement and I think will cost you more than a new wire pull the entire way.
The easy way
This won't seem like the easy way. But that is only because it involves crafts you are unfamiliar or uncomfortable with.
This involves not wasting the long length of Rigid conduit and extending it the extra distance to the garage. Enter the garage in the normal way (up the building side then through an LB conduit body). Then run new THWN wire through it; easy peasy.
Dig up the area under the old junction box. Go as deep as you need to in order to expose the old Rigid conduit. Remove the old 90 degree that takes the pipe upwards, and if there's an elbow there you can cut much of it off rather than dig more dirt to swing it. Leave enough meat on it to get a pipe wrench to unscrew it from the coupler.
From there, trench a little the direction you think the conduit is going, and if the wires are gone you can stick a bit of re-rod in there to confirm direction. Plot out where to put a 45 or 90 bend (45 is better) to get over to the garage. This is metal pipe plumbing and will require you cut and thread pipe, but you only have to trench 8" (to give 6" cover).
You'll need one 10' stick of Rigid, one 90 elbow and possibly one 45. Possibly a nipple or another stick. Rigid is expensive but this little of it is cheap. It'll allow you to use 2xTHWN-2 instead of expensive UF.
It's good to either have a pipe vise and a RiDgid threader, or make a couple runs to the hardware store to have pipe threaded to length... The last one will be somewhat critical, though if you approach the wall at an angle that will make it much less critical, don't select the thru-wall location until the piping has reached it. And don't line up on a joist.
It's a lot of work but its also 90% of the work. Terminate indoors in a steel junction box. Now you pull a black and white THWN-2 and you're done. Very easy pull especially with stranded THWN. Pull the ground off the metal box.
And you have expansion room to blow it out to a MWBC (one more wire) or even pull bigger wire for a subpanel.
The hard way
You can use the Rigid conduit essentially as a wire guard (not as proper conduit) but this will mean running continuous UF all the way from house to garage, and worse, pulling Cable through long conduit, which is the mark of the amateur. You cannot reuse whatever THWN wire is in the conduit now.
You will need to extend the Rigid downward to the 25" depth so the direct burial cable can exit the conduit at a depth that is legal for it. You can
- back-trench the 10-20 feet of existing Rigid conduit so you can bend it downwards so its exit is at 25" depth for 24" cover.
- add two 90's and a nipple to drop the Rigid straight down, but this will mean at least three 90’s in this pull, which will make it a challenge.
- add two 45’s and a longer nipple, which will solve the pull problem but put you much closer to the garage, almost defeating the purpose of not just doing it the easy way (what is that purpose anyway?)
Then you trench at 25" to the garage, where you must use more conduit (90 and stick and LB) as a guard/shield to protect the UF as it rises from 25" depth, then come up the side of the garage to an LB conduit body and on into the garage.
So you still need a whole bunch of conduit, and more of the weird parts... and you only get to run in open dirt for a few feet. You must really like trenching to use this option.
And worse, you have left the customer much worse off than the other option. This provides only for a single #12 circuit and it can never be upgraded. If he ever wants more power in the garage, he's likely to be unaware he could just dig up in the right place and insert the missing 6-7 feet of conduit and have proper conduit the whole way. Not knowing that, he'd just trench a completely new cable.
Honestly this option just seems dumb.