Sounds great! (Male start)

TL;DR - Jake gets fabric, it turns into outfits, if someone else puts it on, they believe they are whatever the outfit looks like, and acts as such. They make up happy, believable memories to fill time gap when they take off the outfit, and the fabric then returns to its shape as a small little piece.

"I'm Jake. Nice to meet you"
"Nice to meet you Jake! Shall we?"
Jake stands up, shake the person's hand, and begins following them back to their workshop. They invite him inside, and both sit at a large wooden table that looks centuries old. Jake turns his head for no more than two seconds, to look at some machinery, and when he looks back, a warm cup of coffee is in front of him on the table. It smells like his favorite brew, and wouldn't you know it, tastes like it, too!

The person cleared their throat and began speaking.

"So Jake, today is probably the luckiest day of your life. What you have there is something I call 'Infinity Fabric'. I heard it on the internet once... Liked the name." They chuckle "But the name isn't important. It's what it does, that is. The fabric you hold in your hands is a wonder that I've spent somewhere around... oh, maybe 538 years, give or take a few, working on. But we agreed to get acquainted first! I know you, but you don't know me..." They state, ominously.
"You may have noticed that you can't really tell if I'm man or woman or even human. My voice is androgynous, my face is nearly impossible to make out even staring at it in perfect lighting, and my body language is as normal as one can get. That's because I'm probably over a millennia old now. I've lost track of my own age. I'm not sure I'm human anymore, but judging by how much magic and technology I've dabbled in, I'd say most likely not... which would explain why you, nor anyone else, can really tell who or what I am. Don't worry about my name either, I've not even uttered it in at least a century or two, it means nothing to me." They say as you state in bewilderment. But unless you were , hypnotized, or in the Matrix... You have no counter-argument.
They continue, saying "in my youth, I was the apprentice to a wizard who specialized in enchantments, specifically ones related to clothing and armor. I was his prodigy, and together, we developed magics you wouldn't believe. As time went on, he began aging faster, and I, slower. Something makes me wonder if it was a particular combination of enchantments we each had on our clothing at the time, but I can't say for sure. Maybe we performed some incantations incorrectly..."
"Anyway! As the years went on, I once heard an individual I quite respected say 'clothes maketh the man' and I thought to myself '_What if that were true?' _I understood the idiom, but I wanted it to be more literal. I imagined clothing, that truly did make the wearer what they were. Or, believed they were, at least. So I began my research. I began with what I already knew; magic. But as time wore on, my master was becoming more aged and weary, and could no longer aid me in my endeavor. He passed at the ripe old age of 1,437. A few centuries went by, and I saw the rise of machinery. But where normal humans used them for manufacturing, and transportation, I used them for enhancing my magic. Then, I turned my magic on the machines. After the year... 1960 or so... I discovered the concept of computers. I quite liked the idea, and began using them in tandem with my existing inventions. Long before regular humans figured out nanotechnology, I had mastered it, thanks to my use of magic with these machines. I figured out how to make them smaller and smaller until I could fit a whole computer inside a grain of sand. Then, I began weaving them into my cloths. It wasn't until a few months ago, that I got the programming synced up perfectly with the magic to create this fabric. And I was just in the process of producing proper samples when some tore off and flew out the window. And the rest is our own personal history!"

Jake just sat in awe. This was almost too much to take in. The person (ascended being?) was acutely aware of this, and offered the last bit of the promised explanation.
"Let me tell you what the fabric does." They say firmly. "It takes the form of whatever its designated owner dreams up while holding it. It can fit any person exactly as imagined, and not only can multiply or create more of itself from just a small scrap like what you're holding, but it returns to that shape and size when it is 'turned off' so to speak. While being worn, it feels perfectly comfortable, keeps the wearer's temperature in check, and offers protection from mild dangers or impacts. But it's far from bullet-proof. But most importantly, if not being worn by the designated owner, and it's taken the form of a costume or other outfit intended for someone of a particular persona, the wearer will believe, wholly and fully, that they are that person or entity, and think of nothing else but behaving like that entity. The wearer will gain very minor semblance of the skills and knowledge of the persona they portray. They won't remember a thing they did during all this, and will fabricate a believable and pleasant memory to fit the time gap. If you offer someone to let them try on the outfit, they'll desperately want to do so."
"I offer, if you accept my proposal, to keep that piece you have there, and become its owner. In exchange, you bring it back to me every so often to check on it, read its data, and repair it should damage occur. Does that sound like a good deal?"

"Y-yes!! absolutely!" Jake croaks out anxiously.

"Marvelous! I've completed my life's work and I can retire! I can enjoy myself, maybe make some friends for the first time in I-don't-know-how-long. I'll settle down right here in this town, and send you an update on my location! I'm sure you can't wait to test it out, so you get on out of here! I'm sure we'll be seeing each other soon enough, young man! Oh, and sorry I spent all our time together talking. Next time, you'll get that opportunity."

It didn't take long for Jake to walk out the door and start walking.