Just use one mobile phone as the server and another mobile phone as the client.
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Mobile server micro-architecture design and implementation

Yes, to put it simply, at least one of the two devices supports OTG.
There is a better answer on StackOverFlow. I quoted it. In order to prevent the link from opening, I put the quote here:

It is possible between some phones.

But at least one of them must have OTG support. and you need an OTG
connector.(also a USB cable) Check the following link for detailed
explanation:

http://forum.xda-developers.c...

I'll be quoting the detailed explanation just in case the link gets
broken:

Yes if u need to transfer data between two phones like GBs of data n u
u have atleast one phone that supports OTG and u been looking for pc
to transfer data or been trying to use wifi share apps trust me this
is a solution to npc-less transfers and EVEN U CAN BORTOW YOUR FRIENDS
BATTERY CHARGE IF YOU ARE RUNNING LOW ON BATTERY!!!!!!

With just an OTG n a USB cable you CAN transfer data and battery
charge between two phones!!

you need:

A) 2 phones (at least one with OTG support)

B)OTG connector

C)Usb cable.

D)file explorer like es file explorer

Here on il refer the phone that contains data and charge as "host"
phone n to phone to be transferred as "second" phone.

If your second phone is a xperia device then go to settings ->xperia
connectivity ->usb connectivity

Change the usb connectivity mode from "MTP" to "MSC"..

Steps:

1)Just connect OTG cable to host phone...

2)The second phone connect usb cable.. N the pc usb part.. Which u
connect to pc...connect it to the OTG

REMEMBER 3)In the second phone select ur mass storage option!!

4) use file explorer (I used Es file explorer coz its the best I used)

BINGO.. On host phone u can see the memory card of second phone as
"usbdisk"...plus.. The second phone will charge battery from first
phone...

Worked on

my xperia Z1 as host and micromax a65 as second phone..

my xperia Z1 as host and micromax a116 as second phone..

my xperia Z1 as host and xperia M as second phone..

my xperia M as host and xperia z1 as second phone..

Well all permutations of these phones..

Reference: Connect two Android phones with USB cable