I think it was closer to 3 months to prepare for the repair a five weeks estimated repair time. Perhaps a good deal of the three months was putting into action a well-researched operation, but Boeing did apparently build a whole new rear fuselage barrel to cut the repair patch from. I presume this would have taken quite a while,
Presumably the need to cut out of a new whole section is to preserve the pre-stressing inherent in the manufacture of a whole section? Obviously they wouldn't have done so if a section could have been laid by itself, so it must presumably must be in order to match the original. I presume that the problem is strain rather than stress and that the composite is anisotropic - i.e. the Young's modulus is not the same in all directions. This would affect the natural frequency of the section and it's possible that unexpected resonances would show up after completion of the repair. Resonances are likely to be a greater risk than absolute strength.
I wonder what this tells us about the cost and time to repair less sensational cases such as collision damage on the ground. Could be very expensive for the insurers.
....and in the mean time they had to plan/hire/build the shelter and heating/ventilation equipment. There is quite a lot of "stuff" there; sourcing, making and/or hiring all of that would take a while, especially as composites need controlled stable environments, and winter at LHR is hardly stable!
Many composites need stable environments when curing and until the final seal is applied (to prevent ingress of water) but a panel from the factory should be fine to handle. Obviously the outside and inside surfaces are completely safe as they are designed to resist moisture, ice, glycol, salt and common cleaning fluids and I presume that the edges will have been treated with a suitable sealant. The prepared edges of the a/c hull section are susceptible to ingress of water though environmental control beyond a normal maintenance hangar is unlikely to be needed. A plastic tent around a given section is a well-established technique and can be set up over a weekend. If it needs more than that I would be surprised.