Datum transformation in QGIS 3

Question

I have an Esri shapefile with following in the .prj file (broken into multiple lines for comprehension):

PROJCS[
  "SGL_Stereo",
  GEOGCS[
    "GCS_SGL_GEO",
    DATUM[
    "D_SGL",
    SPHEROID["Clarke_1880_IGN", 6378249.2,293.4660212936265]],
    PRIMEM["Greenwich",0.0],UNIT["Degree",0.0174532925199433]],
    PROJECTION["Double_Stereographic"],
    PARAMETER["False_Easting",0.0],
    PARAMETER["False_Northing",0.0],
    PARAMETER["Central_Meridian",39.15],
    PARAMETER["Scale_Factor",0.9995341],
    PARAMETER["Latitude_Of_Origin",34.2],
    UNIT["Meter",1.0]
]

The problem is that this is a non-standard projection, so any data that I get from the internet, especially that in WGS84, is misaligned, even after re-projecting it.

I found a solution for this, which includes a datum transform. When I try to add a custom datum transform in QGIS (Properties -> CRS -> Datum transformations -> Add), what I see is the following:

I select the source CRS, and match it with WGS84, but I get no further options to enter the parameters of the transformation.

What am I missing?

Answer 1

(Edited answer)

Your map projection is the Deir ez Zor / Levant Stereographic projection (EPSG 22780)

https://epsg.io/22780-15742

   +proj=sterea +lat_0=34.2 +lon_0=39.15 +k=0.9995341 +x_0=0 +y_0=0  
   +a=6378249.2 +b=6356515 +towgs84=-190.421,8.532,238.69,0,0,0,0 
   +units=m +no_defs 

As for your second question: tick the box next to "Ask for datum transformation if several are available" . If you now apply the levant stereo crs to your data you'll be prompted for a set of transformation parameters, the best matching for Lebanon so far is

    +towgs84=-190.421,8.532,238.69,0,0,0,0

You can add this string also in de box for default transformation for new projects if you want to work default in Levant stereo in new projects.

An alternative approach would be to take the default settings (do not prompt, do not ask) and create a custom made crs with transformation

   +proj=sterea +lat_0=34.2 +lon_0=39.15 +k=0.9995341 +x_0=0 +y_0=0  
   +a=6378249.2 +b=6356515 +towgs84=-<your-X>,<your-Y>,<your-Z>,0,0,0,0 
   +units=m +no_defs