Entites like inserters, loaders and such loose the configuration of conditions and filters.

while trying to reproduce this in a small scale i noticed, that circuit wires vanish which are connected to the loader.

The conditions which get lost are conditions within the logistic network

an moved entity of "Improved inventory sensor" stopped showing the inventory of the adjacent chest ... because it still looks at the old location, need to report this to the mod author. Does a moved entity gets an event about being at a new location?

There is an issue for loaders. But inserters are working properly (standard teleport is used)

For loader, it is fixed in 1.05. For other mods, there is an api to subscribe to move events.

oops, i tried to teleport the same group as before, now the game crashes:

Exception at tick 169959975: The mod Factory organizer (1.0.5) caused a non-recoverable error.
Please report this error to the mod author.

Error while running event factory_organizer::on_gui_click (ID 1)
Writing to LuaEntity::loader_belt_stack_size_override requires the loader to have adjustable_belt_stack_size enabled.
stack traceback:
[C]: in function 'newindex'
__factory_organizer/scripts/main.lua:729: in function 'apply'
factory_organizer/scripts/main.lua:1017: in function 'teleport'
factory_organizer/scripts/main.lua:1190: in function 'handler'
factory_organizer/scripts/tools.lua:426: in function <factory_organizer/scripts/tools.lua:422>

I get it. Is caused by loaders that does not support stacking , such as deadlock's. Should be fixed in 1.0.6

ok, the small group was teleported without problems beside those inventory sensors, but then i tried to move a much more bigger chunk of my factory:

Exception at tick 171137270: The mod Factory organizer (1.0.6) caused a non-recoverable error.
Please report this error to the mod author.

Error while running event factory_organizer::on_gui_click (ID 1)
factory_organizer/scripts/main.lua:1033: attempt to index local 'belt' (a nil value)
stack traceback:
factory_organizer/scripts/main.lua:1033: in function 'teleport'
factory_organizer/scripts/main.lua:1192: in function 'handler'
factory_organizer/scripts/tools.lua:426: in function <factory_organizer/scripts/tools.lua:422>

thank you very much, 1.0.7 did it.