Can't boot Windows 7 from Ubuntu 12.04 boot menu and vice-versa

Question

I have installed Windows 7, then ubuntu on a 64 bit laptop and I have an issue with dual boot : Windows does not see ubuntu partition, and grub displays "Invalid EFI file path" as described on a askubuntu question

If I enter the boot option and I choose windows bootloader, windows will both successfully. Likewise, if I choose ubuntu I can load ubuntu correctly. I want to load either OS from the bootloader of the other.

The drive is partitioned as:

(parted) print
Model: ATA ST9750420AS (scsi)
Disk /dev/sda: 750GB
Sector size (logical/physical): 512B/4096B
Partition Table: gpt

Number  Start   End    Size    File system     Name                          Flags
 1      1049kB  211MB  210MB   fat32           EFI system partition          boot
 2      211MB   345MB  134MB                   Microsoft reserved partition  msftres
 3      345MB   300GB  300GB   ntfs            Basic data partition
 4      300GB   673GB  373GB   ntfs            Basic data partition
 6      673GB   673GB  1049kB
 7      673GB   717GB  44.0GB  ext4
 8      717GB   723GB  6322MB  linux-swap(v1)  LINUXSWAP
 5      723GB   750GB  26.8GB  ntfs            Basic data partition          hidden,diag

Answer 1

I have not yet solved the problem itself, but avoided it. I installed another boot manager where I can select either linux or windows boot loaders. It works fine, it is pretty straightforward to install from linux, and it is called rEFInd.