LibLinphone handle file transfer following the Rich Communications Services recommendations : http://www.gsma.com/network2020/wp-content/uploads/2015/03/RCS5.3_UNI.zip RCC.07 v6.0.pdf section 3.5.4.8 File Transfer via HTTP.
Flexisip, a flexible SIP proxy server with media capabilities.
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If you use your own server, make sure to have the directory storing the uploaded file unable to serve php or any other script language files and/or filter on file extension.