Difficulty in linking FFTW library with gfortran - g++

Question

I have a c++ program, which uses the FFTW3 library, which I would like to translate to Fortran. I am using Ubuntu 22.04.1.
I installed the FFTW3 library as detailed in Installation on UNIX
The c++ main program is named ksbenchmark.cpp and, using g++, I compile it and link it (to the math and fftw3 libraries) with
g++ -o my_executable.out ksbenchmark.cpp -lm -lfftw3
which works great.
I have translate the c++ code in Fortran, the source file being named ksbenchmrk.f90.
If I issue
gfortran ksbenchmark.f90 -lfftw3 -lm
I get error messages
/usr/bin/ld: /tmp/cca2xMGa.o: in function `ksintegrate_':
ksbenchmark.f90:(.text+0x59): undefined reference to `dfftw_plan_dft_1d_'
/usr/bin/ld: ksbenchmark.f90:(.text+0x94): undefined reference to `dfftw_plan_dft_1d_'
/usr/bin/ld: ksbenchmark.f90:(.text+0xcf): undefined reference to `dfftw_plan_dft_1d_'
/usr/bin/ld: ksbenchmark.f90:(.text+0x4de): undefined reference to `dfftw_execute_'
/usr/bin/ld: ksbenchmark.f90:(.text+0x5db): undefined reference to `dfftw_execute_'
/usr/bin/ld: ksbenchmark.f90:(.text+0x626): undefined reference to `dfftw_execute_'
/usr/bin/ld: ksbenchmark.f90:(.text+0x780): undefined reference to `dfftw_execute_'
/usr/bin/ld: ksbenchmark.f90:(.text+0xa1c): undefined reference to `dfftw_execute_'
collect2: error: ld returned 1 exit status
I have spent the afternoon reading about it, and it seems I may have to use -I and -L flags such as
gfortran test.f90 -L/new/path/to/lib -I/new/path/to/include -lfftw3 -lm
as illustrated in the post Problems linking FFTW with gfortran (symbol(s) not found for architecture x86_64).
The first question is, what paths to use?
I can find files referring to fftw3 in /usr/local/lib as well as in /usr/local/include, but the attempt
gfortran ksbenchmark.f90 -L/usr/local/lib -I/usr/local/include -lfftw3 -lm
returns the same error as before
/usr/bin/ld: /usr/lib/gcc/x86_64-linux-gnu/11/../../../x86_64-linux-gnu/Scrt1.o: in function `_start':
(.text+0x1b): undefined reference to `main'
/usr/bin/ld: /tmp/ccW2DYGP.o: in function `ksintegrate_':
ksintegrate.f90:(.text+0x62): undefined reference to `dfftw_plan_dft_1d_'
/usr/bin/ld: ksintegrate.f90:(.text+0x9d): undefined reference to `dfftw_plan_dft_1d_'
/usr/bin/ld: ksintegrate.f90:(.text+0xd8): undefined reference to `dfftw_plan_dft_1d_'
/usr/bin/ld: ksintegrate.f90:(.text+0x4df): undefined reference to `dfftw_execute_'
/usr/bin/ld: ksintegrate.f90:(.text+0x5f7): undefined reference to `dfftw_execute_'
/usr/bin/ld: ksintegrate.f90:(.text+0x643): undefined reference to `dfftw_execute_'
/usr/bin/ld: ksintegrate.f90:(.text+0x79d): undefined reference to `dfftw_execute_'
/usr/bin/ld: ksintegrate.f90:(.text+0xa5b): undefined reference to `dfftw_execute_'
collect2: error: ld returned 1 exit status
I am unable to understand which paths to the library are to be used.
How to find where the library is saved?
Why does not g++ need any paths to the library?
I apologise for how trivial the question might seem, I am a total newbie can ensure I put a significant effort in trying to sort this out. Any hint would be most appreciated, thanks
EDIT
Following Vladimir F Героям слава's advice, I tried using the nm command to verify the library contains what is expected to.
In /usr/local/lib
I found libfftw3.a and libfftw3.la files.
Issuing nm libfftw3.a I get quite a long list.
I tried looking for one of the commands I get an error about, dfftw_plan_dft_1d
nm -S libfftw3.a | grep dfftw_plan_dft_1d
and indeed it returns hits
00000000000003a0 0000000000000026 T _Z18dfftw_plan_dft_1d_PP11fftw_plan_sPiPA2_dS4_S2_S2_
0000000000002df0 0000000000000026 T _Z19dfftw_plan_dft_1d__PP11fftw_plan_sPiPA2_dS4_S2_S2_